Class 8th Mathematics AP Board Solution
Exercise 4.1- 4−3 Simplify and give reasons
- (−2)^7 Simplify and give reasons
- Simplify and give reasons
- (−3)−4 Simplify and give reasons
- (−2)^7 × (−2)^3 × (−2)^4 Simplify the following:
- (1/2)^4 x (1/2)^5 x (1/2)^6 Simplify the following:
- Simplify the following: 4^4 (5/4)^4
- (5^-4/5^-6) ×5^3 Simplify the following:
- (−3)^4 × 7^4 Simplify the following:
- 2^2 × 3^2/2^-2 ×3-1 Simplify
- (4−1 × 3−1) ÷ 6−1 Simplify
- (4^0 + 5−1) ×5^2 × 1/3 Simplify and give reasons
- (1/2)^-3 x (1/4)^-3 x (1/5)^-3 Simplify and give reasons
- (2−1 + 3−1 + 4−1) × 3/4 Simplify and give reasons
- 3^-2/3 ×(3^0 -3-1) Simplify and give reasons
- 1 + 2−1 + 3−1 + 4^0 Simplify and give reasons
- [(3/2)^-2]^2 Simplify and give reasons
- [(3^2 - 2^2) / 1/5]^2 Simplify and give reasons
- ((5^2)^3 × 5^4) ÷ 5^6 Simplify and give reasons
- (2/3)^3 x (2/3)^5 = (2/3)^n-2 Find the value of ‘n’ in each of the following:…
- (−3)n+1 × (−3)^5 = (−3)−4 Find the value of ‘n’ in each of the following:…
- 72n+1 ÷ 49 = 7^3 Find the value of ‘n’ in each of the following:
- Find ‘x’ if 2^-3 = 1/2^x
- Simplify [(3/4)^-2 / (4/5)^-3] x (3/5)^-2
- 9m^2 - 10n^3 If m = 3 and n = 2 find the value of
- 2m^2 n^2 If m = 3 and n = 2 find the value of
- 2m^3 + 3n^2 - 5m^2 n If m = 3 and n = 2 find the value of
- mn - nm If m = 3 and n = 2 find the value of
- Simplify and give reasons (4/7)^-1 x (7/4)^-7
Exercise 4.2- 0.000000000947 Express the following numbers in the standard form.…
- 543000000000 Express the following numbers in the standard form.
- 48300000 Express the following numbers in the standard form.
- 0.00009298 Express the following numbers in the standard form.
- 0.0000529 Express the following numbers in the standard form.
- 4.37 × 10^5 Express the following numbers in the usual form.
- 5.8 ×10^7 Express the following numbers in the usual form.
- 32.5 × 10−4 Express the following numbers in the usual form.
- 3.71529 × 10^7 Express the following numbers in the usual form.
- 3789 × 10−5 Express the following numbers in the usual form.
- 24.36 × 10−3 Express the following numbers in the usual form.
- Size of the bacteria is 0.0000004 m Express the following information in the…
- The size of red blood cells is 0.000007mm Express the following information in…
- The speed of light is 300000000 m/sec Express the following information in the…
- The distance between the moon and the earth is 384467000 m (app) Express the…
- The charge of an electron is 0.0000000000000000016 coulombs Express the…
- Thickness of a piece of paper is 0.0016 cm Express the following information in…
- The diameter of a wire on a computer chip is 0.000005 cm Express the following…
- In a pack, there are 5 books, each of thickness 20 mm and 5 paper sheets each of…
- x-3 × x-2 = x-6 Rakesh solved some problems of exponents in the following way.…
- (x^2)^3 = 3x^-1 = 1/3x root x = x^8/x^2 = x^4 Rakesh solved some problems of…
- (x^2)^3 = x^2^3 = x^6 Rakesh solved some problems of exponents in the following…
- x^-2 = root x Rakesh solved some problems of exponents in the following way. Do…
- 3x^-1 = 1/3x Rakesh solved some problems of exponents in the following way. Do…
- 4−3 Simplify and give reasons
- (−2)^7 Simplify and give reasons
- Simplify and give reasons
- (−3)−4 Simplify and give reasons
- (−2)^7 × (−2)^3 × (−2)^4 Simplify the following:
- (1/2)^4 x (1/2)^5 x (1/2)^6 Simplify the following:
- Simplify the following: 4^4 (5/4)^4
- (5^-4/5^-6) ×5^3 Simplify the following:
- (−3)^4 × 7^4 Simplify the following:
- 2^2 × 3^2/2^-2 ×3-1 Simplify
- (4−1 × 3−1) ÷ 6−1 Simplify
- (4^0 + 5−1) ×5^2 × 1/3 Simplify and give reasons
- (1/2)^-3 x (1/4)^-3 x (1/5)^-3 Simplify and give reasons
- (2−1 + 3−1 + 4−1) × 3/4 Simplify and give reasons
- 3^-2/3 ×(3^0 -3-1) Simplify and give reasons
- 1 + 2−1 + 3−1 + 4^0 Simplify and give reasons
- [(3/2)^-2]^2 Simplify and give reasons
- [(3^2 - 2^2) / 1/5]^2 Simplify and give reasons
- ((5^2)^3 × 5^4) ÷ 5^6 Simplify and give reasons
- (2/3)^3 x (2/3)^5 = (2/3)^n-2 Find the value of ‘n’ in each of the following:…
- (−3)n+1 × (−3)^5 = (−3)−4 Find the value of ‘n’ in each of the following:…
- 72n+1 ÷ 49 = 7^3 Find the value of ‘n’ in each of the following:
- Find ‘x’ if 2^-3 = 1/2^x
- Simplify [(3/4)^-2 / (4/5)^-3] x (3/5)^-2
- 9m^2 - 10n^3 If m = 3 and n = 2 find the value of
- 2m^2 n^2 If m = 3 and n = 2 find the value of
- 2m^3 + 3n^2 - 5m^2 n If m = 3 and n = 2 find the value of
- mn - nm If m = 3 and n = 2 find the value of
- Simplify and give reasons (4/7)^-1 x (7/4)^-7
- 0.000000000947 Express the following numbers in the standard form.…
- 543000000000 Express the following numbers in the standard form.
- 48300000 Express the following numbers in the standard form.
- 0.00009298 Express the following numbers in the standard form.
- 0.0000529 Express the following numbers in the standard form.
- 4.37 × 10^5 Express the following numbers in the usual form.
- 5.8 ×10^7 Express the following numbers in the usual form.
- 32.5 × 10−4 Express the following numbers in the usual form.
- 3.71529 × 10^7 Express the following numbers in the usual form.
- 3789 × 10−5 Express the following numbers in the usual form.
- 24.36 × 10−3 Express the following numbers in the usual form.
- Size of the bacteria is 0.0000004 m Express the following information in the…
- The size of red blood cells is 0.000007mm Express the following information in…
- The speed of light is 300000000 m/sec Express the following information in the…
- The distance between the moon and the earth is 384467000 m (app) Express the…
- The charge of an electron is 0.0000000000000000016 coulombs Express the…
- Thickness of a piece of paper is 0.0016 cm Express the following information in…
- The diameter of a wire on a computer chip is 0.000005 cm Express the following…
- In a pack, there are 5 books, each of thickness 20 mm and 5 paper sheets each of…
- x-3 × x-2 = x-6 Rakesh solved some problems of exponents in the following way.…
- (x^2)^3 = 3x^-1 = 1/3x root x = x^8/x^2 = x^4 Rakesh solved some problems of…
- (x^2)^3 = x^2^3 = x^6 Rakesh solved some problems of exponents in the following…
- x^-2 = root x Rakesh solved some problems of exponents in the following way. Do…
- 3x^-1 = 1/3x Rakesh solved some problems of exponents in the following way. Do…
Exercise 4.1
Question 1.Simplify and give reasons
4−3
Answer:Given, = ![](data:image/png;base64,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)
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= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
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Question 2.Simplify and give reasons
(−2)7
Answer:Given, = (
2)7
= -(2×2×2×2×2×2×2 )∵(-2)7=-(2)7
=
128
7=
128
Question 3.Simplify and give reasons
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Answer:Given, =![](data:image/png;base64,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)
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= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACgAAAAhCAMAAACcLxmXAAAAAXNSR0IArs4c6QAAAHhQTFRFAAAAAAAAAAA6AABmADo6ADqQOgAAOgA6OjoAOma2OpDbZgA6Zjo6ZjpmZjqQZpDbZra2ZrbbZrb/kDoAkDo6kGY6kGaQkLbbkNv/tmYAtmY6tmZmtv//25A625Bm27Zm27aQ29uQ2////7Zm/9uQ/9u2//+2///brcCVPAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAzUlEQVQ4T8WU6Q6CMBCEB9SKtxwqKngiff83dHcBxaSb+Id0E0jzZTK7bRmAIaoyya+tAmwWsfDEr3r9ADRQxqlolgk9Oa0U8JxZEZJqS1pAAfWqsGm8p46ozJz1boAy4JqQsHVUAPdsWvN8PKcOcDejAjjzPmTXTjDEvfjzlGP8o/xN6LfzJQrCTX8EBdjsgGtIX06XGQWIVTUl4TczTsC61y7uZ0YFx2AswjYzgA5u8gfoUkhLB0C9yMmKhF1mFABcTHM8n8yowNc1vgF+ihw6SvkfNAAAAABJRU5ErkJggg==)
=![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 4.Simplify and give reasons
(−3)−4
Answer:Given, =(
3)-4
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAiCAMAAAC3OnOQAAAAAXNSR0IArs4c6QAAAEhQTFRFAAAAAAAAAGaQAGa2OgAAOmZmOmaQOma2OpDbZgAAZjoAZrbbZrb/kDoAtmYAtmY625A625Bm27Zm2////9uQ/9u2//+2///b77fSgwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAcklEQVQoU6WQSRKAIAwEg6IsCqII/P+nEpYST1ZBbkNmSNIAXRWOuc2di/xoADOmg55sM8CQWLxr078Q/tzUn3287yQhKx6XGQbFwYl4W2HoxQ6gE73EMChmHb5VpphnCU7qe7lFz+u/adWF4UXzvD6GDwvlBCRke0X9AAAAAElFTkSuQmCC)
(
3)-4= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAiCAMAAAC3OnOQAAAAAXNSR0IArs4c6QAAAEhQTFRFAAAAAAAAAGaQAGa2OgAAOmZmOmaQOma2OpDbZgAAZjoAZrbbZrb/kDoAtmYAtmY625A625Bm27Zm2////9uQ/9u2//+2///b77fSgwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAcklEQVQoU6WQSRKAIAwEg6IsCqII/P+nEpYST1ZBbkNmSNIAXRWOuc2di/xoADOmg55sM8CQWLxr078Q/tzUn3287yQhKx6XGQbFwYl4W2HoxQ6gE73EMChmHb5VpphnCU7qe7lFz+u/adWF4UXzvD6GDwvlBCRke0X9AAAAAElFTkSuQmCC)
Question 5.Simplify the following:
(−2)7 × (−2)3 × (−2)4
Answer:Given, = (−2)7 × (−2)3 × (−2)4
= (−2)7+3+4 ![](data:image/png;base64,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)
= (−2)14
(−2)7 × (−2)3 × (−2)4=(−2)14
Question 6.Simplify the following:
![](data:image/png;base64,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)
Answer:To Find: ![](data:image/png;base64,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)
We know that: am × an = a(m+n)
Therefore,
![](data:image/png;base64,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)
=2-15
Answer.
Question 7.Simplify the following:
44 ×![](data:image/png;base64,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)
Answer:Given, = 44 ×![](data:image/png;base64,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)
= 44![](data:image/png;base64,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)
= 54
= 625
Question 8.Simplify the following:
×53
Answer:Given, =
×53
=
3![](data:image/png;base64,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)
=![](data:image/png;base64,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)
=![](data:image/png;base64,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)
= 56-1![](data:image/png;base64,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)
= 55
= 625
×53 = 625.
Question 9.Simplify the following:
(−3)4 × 74
Answer:Given, = (−3)4 × 74
= ![](data:image/png;base64,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)
= 9
9
2401
= 194,481
(−3)4 × 74= 194,481
Question 10.Simplify
22×
×3-1
Answer:Given, =22×
×3-1
=
(
)
=
(
)
= 24 × 31
= 16 × 3
= 48
22×
×3-1 = 48.
Question 11.Simplify
(4−1 × 3−1) ÷ 6−1
Answer:Given, = (4−1 × 3−1) ÷ 6−1
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAhCAMAAAAieUHKAAAAAXNSR0IArs4c6QAAAE5QTFRFAAAAAAAAAAA6AGaQAGa2OgA6OmZmOma2OpDbZgAAZgA6ZjoAZrb/kLbbkNv/tmYAtmY625A625Bm27Zm29u22////7Zm/9uQ//+2///bgWo6oAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAWUlEQVQoU2NgwACSAiwgMSE2bjDNwCCIn5bkZxYFqWIEAg5M43CIgFQDAdHq4QpFuBkZ2RkYJLh4GYSZ+MDC4qwQWhBivTBQGsSDUGJASoyHQYITZB0PLvsALysCbKWAqqcAAAAASUVORK5CYII=)
(4−1 × 3−1) ÷ 6−1 = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAhCAMAAAAieUHKAAAAAXNSR0IArs4c6QAAAE5QTFRFAAAAAAAAAAA6AGaQAGa2OgA6OmZmOma2OpDbZgAAZgA6ZjoAZrb/kLbbkNv/tmYAtmY625A625Bm27Zm29u22////7Zm/9uQ//+2///bgWo6oAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAWUlEQVQoU2NgwACSAiwgMSE2bjDNwCCIn5bkZxYFqWIEAg5M43CIgFQDAdHq4QpFuBkZ2RkYJLh4GYSZ+MDC4qwQWhBivTBQGsSDUGJASoyHQYITZB0PLvsALysCbKWAqqcAAAAASUVORK5CYII=)
Question 12.Simplify and give reasons
(40 + 5−1) ×52 ×![](data:image/png;base64,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)
Answer:Given, =(40 + 5−1) ×52 ×![](data:image/png;base64,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)
=(1+
)
52![](data:image/png;base64,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)
=
52![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABgAAAAhCAMAAAD03JuvAAAAAXNSR0IArs4c6QAAAHhQTFRFAAAAAAAAAAA6ADo6ADpmADqQAGaQAGa2OgAAOgA6OjoAOmZmOma2OpDbZgAAZgA6ZjoAZjpmZmaQZpDbZrbbZrb/kDoAkDo6kGY6kLbbkNv/tmYAtmY6tv//25A625Bm27Zm27aQ29u22////9uQ/9u2//+2///bTqrvEQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAqElEQVQ4T7WSxw7CMBBE16Ek9NAMJBADcfn/P8RNEMyIQwRzWdnPszsrmegXMuccthGzEgOi5v/A1OMWxWqY1eLL3np98VTF+nxq+NARvZynbsNHrb0HS1lyL3MUxHBmTVEuk5U/vYHOJN/qZenECsPTIT6Ui5vGUpvwVMba4w+IKcu2wGcOJ7pmFe4oJxio4w4aajbAgOhW7D8telWRRIBEgeP22DxYHlaoCmpUEOmNAAAAAElFTkSuQmCC)
= 2
52-1
= 2
5
= 10
(40 + 5−1) ×52 ×
= 10
Question 13.Simplify and give reasons
![](data:image/png;base64,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)
Answer:Given, = ![](data:image/png;base64,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)
![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= 23
43
53![](data:image/png;base64,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)
= 23
(22)3
53![](data:image/png;base64,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)
= 23
26
53
= 23+6
53![](data:image/png;base64,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)
= 29
53
= 29
53
Question 14.Simplify and give reasons
(2−1 + 3−1 + 4−1) ×![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAA1CAYAAACjpdDnAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAF6SURBVFjD7ZY/bsIwFMZfd3oAKtyNA5CXXiG1Klakkog1Q4SyMGSqTLZIFRfoxtalcxdOwBngBj0DaZ4baKhwGsdekBLpk7L4l/h97x+kaQq2BB3MPqx4bkhGMBFPhw6DbQE6SDFnO43FUBsmYj5C5K9hlvXOwbifCdFvDMuysOeh93IEVT/AAL4wWI6NDbAK8xHWgP7ayM0omjgyXi7/+Hv1xjCKHR/ApnQzJzH0V3XAf/+MoHHw8EzxkkBvvrBmQF16aJWLNMEWbO6xBQz4RhU3ZT2qDNGKGZUOAuypFidR5BCYQD6yFbmplRp08BHv304FXogx95MH8VPXaTuYDdhxEumoDnbQVedmB1N04FYw2f91F5e2Y64RTIhZv9zTcmOYHCQ8ED+rggFsGeCYJtLv3tESRtdzmftOh41hdD0ei9H5RtQCRmlQndytYTINijhVG2CShLcnWJLcqZJXkZwXG2FeqnjH3aU/bJS0xgZcHWxnDLv+TvsNpuWkkhn+9mcAAAAASUVORK5CYII=)
Answer:Given, = (2−1 + 3−1 + 4−1) ×![](data:image/png;base64,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)
= (
)![](data:image/png;base64,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)
= (
)![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
(2−1 + 3−1 + 4−1) ×
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAiCAMAAAC3OnOQAAAAAXNSR0IArs4c6QAAAHhQTFRFAAAAAAAAAAA6ADo6ADqQAGaQAGa2OgAAOgA6OjoAOjo6OmZmOmaQOma2OpC2OpDbZgA6ZjoAZjo6ZpDbZrbbZrb/kDoAkDo6kGY6kLbbkNv/tmYAtmY625A625Bm27Zm27aQ29u229vb2////9uQ/9u2//+2///bvhObJAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAn0lEQVQoU62Q2w6CMBBEp3ipF6qAWhWoIBT3///QbqkoiQ+aMC/NdNrZ7AH+FpVL/nNbi+jA5zZlT+crqijnxPjcya5Gvrsc/XXICzEbeaCWJ24qFi3wSHJY9kY47d0c2c+bWNz+oYnbv9UFfkCVxW7RwA9U7px78xko9rxIx9mG3wd+Vqrmrj1pnzMvmPnAj7RqifMXvy4VQoUJv2/5BJKYCbkUoNnuAAAAAElFTkSuQmCC)
Question 15.Simplify and give reasons
×(30 -3-1)
Answer:Given, =
×(30 -3-1)
=
)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
×(30 -3-1) = ![](data:image/png;base64,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)
Question 16.Simplify and give reasons
1 + 2−1 + 3−1 + 40
Answer:Given, = 1 + 2−1 + 3−1 + 40
= 1 +
+
+ 1 ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAhCAMAAAAxrgE+AAAAAXNSR0IArs4c6QAAAGBQTFRFAAAAAAAAADqQAGaQAGa2OgAAOjo6OmZmOmaQOma2OpC2OpDbZgA6ZjoAZjo6kDoAkDo6kDqQkNv/tmYAtmY625A625Bm27Zm29u229vb2////7Zm/9uQ/9u2//+2///b8tYltgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAiUlEQVQoU61QSRKDMAxzKFsoENqSLoHW//8ldhbGHBh6QJdEI1saC+AQOOY0g0YR6PesOs9vDnC487Zlzpi0fxKP8sqnOBf1JOPj4vx2kC3nXCkgmJ8Ndhc4237P79XX/sgAHBvBRINRNnVfivm50J+3SS0D/FqqxmarBRrtUOjw7ZTSm4R/71wAkOAGAiK+TywAAAAASUVORK5CYII=)
1 + 2−1 + 3−1 + 40 = ![](data:image/png;base64,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)
Question 17.Simplify and give reasons
![](data:image/png;base64,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)
Answer:Given, = ![](data:image/png;base64,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)
= [
]2
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
Question 18.Simplify and give reasons
![](data:image/png;base64,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)
Answer:Given, = ![](data:image/png;base64,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)
= [(9-4)
5]2
= [5
5]2
= [52]2
= 54
=625
= 625
Question 19.Simplify and give reasons
((52)3 × 54) ÷ 56
Answer:Given, = ((52)3 × 54) ÷ 56
= (56
54)![](data:image/png;base64,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)
= (56
54
5-6)
= 56+4-6
= 54
= 625
((52)3 × 54) ÷ 56 = 625
Question 20.Find the value of ‘n’ in each of the following:
![](data:image/png;base64,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)
Answer:Given, ![](data:image/png;base64,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)
= (![](data:image/png;base64,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)
= (![](data:image/png;base64,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)
= (![](data:image/png;base64,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)
Comparing powers of
, we get
n
2=8
n=8+2
n=10
Question 21.Find the value of ‘n’ in each of the following:
(−3)n+1 × (−3)5 = (−3)−4
Answer:Given, (−3)n+1 × (−3)5 = (−3)−4
(
3)n+1+5 = (−3)−4
(
3)n+6 = (−3)−4
Comparing powers of (
3), we get
n+6 =
4
n =
4
6
n=
10
Question 22.Find the value of ‘n’ in each of the following:
72n+1 ÷ 49 = 73
Answer:Given, 72n+1 ÷ 49 = 73
72n+1
= 73
72n+1
= 73
72n+1
= 73
72n+1-2 = 73
72n– 1 = 73
By comparing powers of 7, we get
2n
1 = 3
2n = 3+1
2n = 4
n = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAhCAMAAAAieUHKAAAAAXNSR0IArs4c6QAAAFpQTFRFAAAAAAAAAAA6AABmADqQOgAAOgA6OjoAOma2OpDbZgAAZgA6ZjoAZjpmZrbbZrb/kDoAkDo6kGaQkLbbkNv/tv//25A627Zm29uQ29u2/7Zm/9uQ//+2///btfclZAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAZ0lEQVQoU42OxxKAIAxEExW7ggVQyv//piTMeJGDe3mTzaYAfOWFJDNuHdOsiuj6SAyLjmrdwSCp4SD3AS5R68K6ssXjiL/zb/CeEfv0x3SArU62fZtpBoZNbaoyXIKTEEY6lx8t6AE8vgPieEWynwAAAABJRU5ErkJggg==)
n = 2
Question 23.Find ‘x’ if ![](data:image/png;base64,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)
Answer:Given, ![](data:image/png;base64,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)
Then, find the value of x.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABUAAAAYBAMAAADnp6t7AAAAAXNSR0IArs4c6QAAAC1QTFRFAAAAAAAAAAA6AABmOgAAZgAAZrb/kDoAkNv/tv//25A625Bm/9uQ//+2///bJjevQwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAMklEQVQoU2NgoB3gTkCYzeOGZM+iBgaGq4JQoIGQ4CueAOeA2NjUgPRCAbKZyHZR00cA9v4I6xisvHwAAAAASUVORK5CYII=)
![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
By comparing the powers of 2, we get
x =
3
x = 3
Question 24.Simplify![](data:image/png;base64,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)
Answer:Given, = ![](data:image/png;base64,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)
= [
] ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAoAAAAYBAMAAAAxAnEeAAAAAXNSR0IArs4c6QAAACRQTFRFAAAAAAAAAAA6ADqQOpDbZgAAkDoAkNv/25A62////9u2///bTGwX7QAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAHUlEQVQYV2NgIA9wJxUANUJIJMAhwrDUkgFCkgUABCcDr0+6mZYAAAAASUVORK5CYII=)
= ![](data:image/png;base64,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)
Question 25.If m = 3 and n = 2 find the value of
9m2 – 10n3
Answer:Given, = 9m2 – 10n3
Where, m = 3 and n = 2
= 9
32
10
23
= (9
9)
(10
8)
= 81
80
= 1
9m2 – 10n3 = 1
Question 26.If m = 3 and n = 2 find the value of
2m2 n2
Answer:Given, = 2m2 n2
m = 3 and n = 2
2m2 n2 = 2
32
22
= 2
9
4
= 72
2m2 n2 = 72
Question 27.If m = 3 and n = 2 find the value of
2m3 + 3n2 – 5m2n
Answer:Given, = 2m3 + 3n2 – 5m2n
= 2
33 + 3
22
5
32
2
= 54 + 12
90
=
24
2m3 + 3n2 – 5m2n =
24
Question 28.If m = 3 and n = 2 find the value of
mn – nm
Answer:Given, = mn – nm
= 32
23
= 9
8
= 1
mn – nm = 1
Question 29.Simplify and give reasons![](data:image/png;base64,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)
Answer:Given, = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHkAAAA/CAYAAADE+2c4AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAWnSURBVHja7Z29bhQ7FMedFGmA2wIXHIkOyqw3okyDFueDggLBrrVCQmgLhEbiQ9oCgZMuguT2lwqqC88QXgBegdDRcV8hlzueZJLZ2ZlZH/t41zPrwkWSndnx/2f/fc6Mz4Ts7OyQ0JrdgggBsscXTshi2uYeYkaLIj1q2Skp+5cZIYdxh44IYd/7Ul6eV8CjWqhGf/FIrtQfcpev3XryqhV3amHeZ7Hsdleyg1wwJvODvnad2t0dnOeUHMSA/2NdeSeAHtWmwzqvB7u752sPOYq2L8mIr1BCfinQAfDJrI41YZ3osdGarGYL1ozRPdfJ5xYL2kK2U5Tyz/mR6zjIWcB0D53z6WihWtRhj/PrsRZkdaJI8A3OxSNbMdUsFJw/4iLaqOpYxpKPxhoTH7Kfu73M3k8r8MLUQlcPiBZFVj0R8nA4uNBjdH9VRPcxxYrE6n3KevuD4fCCizXIRXOlBZYeSZTNhATlyWmnWH9708B+Juau2322qToGtb6sdckuu0N59HxagHW0KLHViTm9qR6nxwu2xcT2ljZk9UWqUyYCPu3Ql3Hu+kPHQiNOn9PO0xeQjikxiuzKpUXranGSs/6Ij/ld3Kp1MdEjkzq9KTt3Se4VzxC6/glqg6+e3GrFEe+/upCV3a5T+snnCBmihZpNKrUrXD/V7ycMSld6lCz09HNRlFZtaf0/GSVfdUZsPuyfdoQMy8n1tRCM7nHxbN3mPKd6WMYrlZDVyIXa4JmliTf8KvkCgXwsDvng42yGaKGsutsthggdyNh6jI+4GFLZAl5paUzspcdDISc2d5V/8Wk2m2pREqe8UGvtrPQYH3Gk9Q0CSNl0m7b/UceYQlazoEXoN+gS4fruEVQLDMt3oYeVVac2nV6MKWQfLdtk2cKMOTD1GPmhx8hHiD0lNpRJLWwgJxbFeh99gQzVAsuqXehhbCvJCG31/som+oPBvT9SyPeGwyuQB/o+RdmmGQbmeTD1yK0DrQPdGagS95J8ME3+QQ/0od/v1KqRrsUGFKYeqCe1sesmQja1aneQEezBBjKWRaJF1hhaWPQHU48A2RHk5BYv6+3POi5wAzl59gnfXNc0yEkKBHyCVwvIPkS0vkD2SY+zjj28fndp6cZhPAMvzijYuXhjaenw+kN5d+aQZ6wFth4BcoBcf8iTNsoV/a25kBu6Jqf7p4pgqm09nLF3+e9s7prcUMhpxJ8HnQBW6V7BQ4gAuYbRdR50Clg9A5+v6LrhKVQKepndfl8FOEA+C1YWoc2HPDnZh6Z2U6pdFxV7qKCQsbXwBfIRtM0acmrRy23+t9oRWbXH2QAyqhbBri0Apxadbn0tAx3sumaQy4Ks0/vsBbsvAuRa5snFQVbyne3225AnNyS6Bt1tCg8o6nVb0+hawr3rAHnuIGPkhE2GrFvK6y1k21LNeYAMKeX1ErJtqWbTIUNLeb2EjFGq2VTIpqW8XkHGLNVsGmTbUl53kKOba+cI/bkl5TWEdQi8qVzKrWuUnPt5M5Jrs8+T7bSwLeXF1mNkZmLs2DdN4ptSQYFRyoutB/odFtO7RU0oeMMs5XVS8HYcSNnXxJrW/6jjpvE2H/2gEq4FZikvph7jKZFFTayNG2DVA2M1qBbYpbyYeqBahLFV+/o6CUBfNEt5D3VmtNPXSaTPWE0t29Sqk1c3UH7g3YthLLSwsWtsPaxtqolWjbp8GUDG1qPwwtTWGPVmeMiJTEs1k+MM3v43rdlsooUNZBd6FI9g9TJP4FvhTEo1k6058ey3KfF0PpsNtMhbvm4p76keyK5WAY3umb7MUzenTNbwiv3P/qRTbrVwrUflKFSdU6MKu3PHLwdffaA65KNNT1OLaeih1blVET3A/PcEdQLsUotp6aH1oWeCr+P+e4Lxx5N1aVhajOoRbbi85loKHVqAHFqAPH/tf24Tb66ADknCAAAAAElFTkSuQmCC)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= (
)2
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAoAAAAYBAMAAAAxAnEeAAAAAXNSR0IArs4c6QAAACRQTFRFAAAAAAAAAAA6ADqQOpDbZgAAkDoAkNv/25A62////9u2///bTGwX7QAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAHUlEQVQYV2NgIA9wJxUANUJIJMAhwrDUkgFCkgUABCcDr0+6mZYAAAAASUVORK5CYII=)
= (
)2
Simplify and give reasons
4−3
Answer:
Given, =
=
=
=
Question 2.
Simplify and give reasons
(−2)7
Answer:
Given, = (2)7
= -(2×2×2×2×2×2×2 )∵(-2)7=-(2)7
= 128
7=
128
Question 3.
Simplify and give reasons
Answer:
Given, =
=
=
=
Question 4.
Simplify and give reasons
(−3)−4
Answer:
Given, =(3)-4
=
=
=
(
3)-4=
Question 5.
Simplify the following:
(−2)7 × (−2)3 × (−2)4
Answer:
Given, = (−2)7 × (−2)3 × (−2)4
= (−2)7+3+4
= (−2)14
(−2)7 × (−2)3 × (−2)4=(−2)14
Question 6.
Simplify the following:
Answer:
To Find:
We know that: am × an = a(m+n)
Therefore,
=2-15
Answer.
Question 7.
Simplify the following:
44 ×
Answer:
Given, = 44 ×
= 44
= 54
= 625
Question 8.
Simplify the following:×53
Answer:
Given, = ×53
= 3
=
=
= 56-1
= 55
= 625
×53 = 625.
Question 9.
Simplify the following:
(−3)4 × 74
Answer:
Given, = (−3)4 × 74
=
= 99
2401
= 194,481
(−3)4 × 74= 194,481
Question 10.
Simplify
22× ×3-1
Answer:
Given, =22× ×3-1
= (
)
= (
)
= 24 × 31
= 16 × 3
= 48
22×
×3-1 = 48.
Question 11.
Simplify
(4−1 × 3−1) ÷ 6−1
Answer:
Given, = (4−1 × 3−1) ÷ 6−1
=
=
=
=
(4−1 × 3−1) ÷ 6−1 =
Question 12.
Simplify and give reasons
(40 + 5−1) ×52 ×
Answer:
Given, =(40 + 5−1) ×52 ×
=(1+)
52
= 52
= 252-1
= 25
= 10
(40 + 5−1) ×52 ×
= 10
Question 13.
Simplify and give reasons
Answer:
Given, =
=
= 2343
53
= 23(22)3
53
= 2326
53
= 23+653
= 2953
= 29
53
Question 14.
Simplify and give reasons
(2−1 + 3−1 + 4−1) ×
Answer:
Given, = (2−1 + 3−1 + 4−1) ×
= ()
= ()
=
=
=
(2−1 + 3−1 + 4−1) ×
=
Question 15.
Simplify and give reasons×(30 -3-1)
Answer:
Given, = ×(30 -3-1)
= )
=
=
=
=
×(30 -3-1) =
Question 16.
Simplify and give reasons
1 + 2−1 + 3−1 + 40
Answer:
Given, = 1 + 2−1 + 3−1 + 40
= 1 + +
+ 1
=
=
1 + 2−1 + 3−1 + 40 =
Question 17.
Simplify and give reasons
Answer:
Given, =
= []2
=
=
=
Question 18.
Simplify and give reasons
Answer:
Given, =
= [(9-4)5]2
= [55]2
= [52]2
= 54
=625
= 625
Question 19.
Simplify and give reasons
((52)3 × 54) ÷ 56
Answer:
Given, = ((52)3 × 54) ÷ 56
= (5654)
= (5654
5-6)
= 56+4-6
= 54
= 625
((52)3 × 54) ÷ 56 = 625
Question 20.
Find the value of ‘n’ in each of the following:
Answer:
Given,
= (
= (
= (
Comparing powers of
, we get
n
2=8
n=8+2
n=10
Question 21.
Find the value of ‘n’ in each of the following:
(−3)n+1 × (−3)5 = (−3)−4
Answer:
Given, (−3)n+1 × (−3)5 = (−3)−4
(3)n+1+5 = (−3)−4
(3)n+6 = (−3)−4
Comparing powers of (
3), we get
n+6 =
4
n =
4
6
n=
10
Question 22.
Find the value of ‘n’ in each of the following:
72n+1 ÷ 49 = 73
Answer:
Given, 72n+1 ÷ 49 = 73
72n+1 = 73
72n+1 = 73
72n+1 = 73
72n+1-2 = 73
72n– 1 = 73
By comparing powers of 7, we get
2n
1 = 3
2n = 3+1
2n = 4
n =
n = 2
Question 23.
Find ‘x’ if
Answer:
Given,
Then, find the value of x.
=
By comparing the powers of 2, we get
x =
3
x = 3
Question 24.
Simplify
Answer:
Given, =
= []
=
=
=
=
=
Question 25.
If m = 3 and n = 2 find the value of
9m2 – 10n3
Answer:
Given, = 9m2 – 10n3
Where, m = 3 and n = 2
= 932
10
23
= (99)
(10
8)
= 81 80
= 1
9m2 – 10n3 = 1
Question 26.
If m = 3 and n = 2 find the value of
2m2 n2
Answer:
Given, = 2m2 n2
m = 3 and n = 2
2m2 n2 = 2
32
22
= 29
4
= 72
2m2 n2 = 72
Question 27.
If m = 3 and n = 2 find the value of
2m3 + 3n2 – 5m2n
Answer:
Given, = 2m3 + 3n2 – 5m2n
= 233 + 3
22
5
32
2
= 54 + 12 90
= 24
2m3 + 3n2 – 5m2n =
24
Question 28.
If m = 3 and n = 2 find the value of
mn – nm
Answer:
Given, = mn – nm
= 32 23
= 9 8
= 1
mn – nm = 1
Question 29.
Simplify and give reasons
Answer:
Given, =
=
=
=
= ()2
= (
)2
Exercise 4.2
Question 1.Express the following numbers in the standard form.
0.000000000947
Answer:Given, = 0.000000000947
= 0.000000000947![](data:image/png;base64,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)
= 9.47 ![](data:image/png;base64,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)
= 9.47 ![](data:image/png;base64,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)
0.000000000947 = 9.47 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEEAAAAYCAMAAACSqGBIAAAAAXNSR0IArs4c6QAAAH5QTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGaQAGa2OgAAOgA6OjqQOmZmOmaQOma2OpDbZgAAZgA6ZjoAZjo6ZjpmZmaQZpDbZrbbZrb/kDoAkGY6kNv/tmYAtmY6ttv/tv//25A625Bm27aQ29u22////7Zm/9uQ/9u2//+2///bMC7tLAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABBklEQVQ4T+1TaxOCIBAUK7OHZfYSM6PyAf//D3Z30KRYNuP0xZnugygsy94uOs5AS519VK4S5h56tXBdRsQg/Lycn3pRwF7YJ8PYUXz9meG21fSglS2yJk4zbACQkpp3VUVsdCEC7uUVh3cZMqqY9NcZ5I6QTmVG+iiDTGiGwoWTCtr3qmYXik8QKsOVpVQzpDjIsCFWpdMclzzjJOq0MaiUGGgRVvH5LIHNgIMyYu6RJgF1j/wahGbrDJqnoxRnbcRvGSwfWmKoi5YIk4VxsuPiGLPgFKtTwyAwSDvNpgjjUkuowIugY/hiZLXXh5dm1PEkM0hsjH8e3E4WdCfRGdN/cUgOPAD9JRf4ce5y7QAAAABJRU5ErkJggg==)
Question 2.Express the following numbers in the standard form.
543000000000
Answer:Given, = 543000000000
= 543000000000 ![](data:image/png;base64,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)
= 5.43
1011
9.47
= 5.43
1011
Question 3.Express the following numbers in the standard form.
48300000
Answer:Given, = 48300000
= 48300000 ![](data:image/png;base64,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)
= 4.83
107
48300000 = 4.83
107
Question 4.Express the following numbers in the standard form.
0.00009298
Answer:Given, = 0.00009298
= 0.00009298 ![](data:image/png;base64,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)
= 9.28 ![](data:image/png;base64,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)
= 9.28 ![](data:image/png;base64,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)
0.00009298 = 9.28 ![](data:image/png;base64,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)
Question 5.Express the following numbers in the standard form.
0.0000529
Answer:Given, = 0.0000529
= 0.0000529 ![](data:image/png;base64,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)
= 5.29 ![](data:image/png;base64,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)
0.0000529 = 5.29 ![](data:image/png;base64,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)
Question 6.Express the following numbers in the usual form.
4.37 × 105
Answer:Given, = 4.37 × 105
= 4.37
100000
= 437000
4.37 × 105 = 437000.
Question 7.Express the following numbers in the usual form.
5.8 ×107
Answer:Given, = 5.8 ×107
= 5.8
10000000
= 58000000
5.8 ×107 = 58000000.
Question 8.Express the following numbers in the usual form.
32.5 × 10−4
Answer:Given, = 32.5 × 10−4
= 32.5 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADkAAAAhCAMAAABUQ/NBAAAAAXNSR0IArs4c6QAAAGNQTFRFAAAAAAAAAAA6ADpmADqQAGaQAGa2OgA6OmZmOma2OpDbZgAAZgA6ZjoAZjpmZmaQZpDbZrbbZrb/kDoAkGY6kNv/tmYAtmY6tv//25A625Bm29u22////9uQ/9u2//+2///b3GOgJQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAA20lEQVRIS+WU6w6CMAyFN8SpIN5QFAW2939KS9cmEiGMJktM7J8vJT1rd0aq1M+GuxvZbM9tIVQqVf+H0lXrRmRurSEykXRUZA8P/N4Rw0925aqX2nwXrqFKV6YNCCVPDdJXYUTeuVJD24/orZwLLP9Sht4Ypx02DZOyQ4svisL+VRab2x19s5YYNmiMKlo87qqTE5jvweR0rDEvnto07eYGuwTBxHRyXlw8Nr/AY2eEYTqj3EOjylgPRfSIphRMS4unStEaAhPTiWl58dhCJ2dwyoPJaYzfIdKZbz9aE+uSLBPXAAAAAElFTkSuQmCC)
= 0.00325
32.5 × 10−4 = 0.00325
Question 9.Express the following numbers in the usual form.
3.71529 × 107
Answer:Given, = 3.71529 × 107
= 3.71529
10000000
= 37152900
3.71529 × 107 = 37152900
Question 10.Express the following numbers in the usual form.
3789 × 10−5
Answer:Given, = 3789 × 10−5
= 3789 ![](data:image/png;base64,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)
= 0.03789
3789 × 10−5 = 0.03789
Question 11.Express the following numbers in the usual form.
24.36 × 10−3
Answer:Given, = 24.36 × 10−3
= 24.36 ![](data:image/png;base64,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)
= 0.02436
24.36 × 10−3 = 0.02436
Question 12.Express the following information in the standard form
Size of the bacteria is 0.0000004 m
Answer:Given, Size of the bacteria is = 0.0000004 m
= 0.0000004 ![](data:image/png;base64,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)
= 4![](data:image/png;base64,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)
= 4 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADoAAAAYCAMAAACcAR4nAAAAAXNSR0IArs4c6QAAAG9QTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOjqQOmaQOma2OpDbZgAAZjoAZjo6ZjpmZmaQZpDbZrb/kDoAkDo6kDqQkGY6kNv/tmYAttv/tv//25A627aQ29u22////7Zm/9uQ/9u2//+2///bftE2MwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAA4UlEQVQ4T+1S2xKCIBCFbpal3SjLLBH4/29sl0UH8fLgNNM00z4IuHv2nD3A2I+EERwimqLWXEtmLrcpUMTI7RjyuafGJuN8k7crR0lVyucPixSrUgnY6wRH5PyMpDSpPtgSptxqD1WcFwSVMyCXFtBETWrEEmt0Esh30Dt20EnLUEdKksIk9CKoTUIWv3V4k0L6lUZeztb4UGrQF3DJ3dSHoMGsnnYU3KFt27QbkEs2BdM4aIH3ElxO4xdZ0NFU4IWSuUMuqSPRVW61B5Ot4eEsTrCFd8XjAX/7Xf///b4DbwCAEe81juIuAAAAAElFTkSuQmCC)
Size of the bacteria is = 4
m
Question 13.Express the following information in the standard form
The size of red blood cells is 0.000007mm
Answer:Given, The size of red blood cells is = 0.000007mm
= 0.000007 ![](data:image/png;base64,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)
= 7 ![](data:image/png;base64,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)
The size of red blood cells = 7
mm
Question 14.Express the following information in the standard form
The speed of light is 300000000 m/sec
Answer:Given, The speed of light is = 300000000 m/sec
= 300000000 ![](data:image/png;base64,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)
= 3.0
108
The speed of light = 3.0
108m/sec.
Question 15.Express the following information in the standard form
The distance between the moon and the earth is 384467000 m (app)
Answer:Given, The distance between the moon and the earth,
= 384467000 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACoAAAAlCAMAAAADS4u8AAAAAXNSR0IArs4c6QAAAG9QTFRFAAAAAAAAAAA6ADpmADqQAGaQAGa2OgAAOgA6OgBmOmZmOma2OpDbZgAAZgA6ZjoAZjpmZmaQZpDbZrbbZrb/kDoAkGY6kNv/tmYAtmY6ttv/tv//25A625Bm27Zm29u22////9uQ/9u2//+2///bTCx8bAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAA6klEQVQ4T9WT2w6CMBBEW0C8gXgBQUGltP//jW63mAjabkl40H1p0pxMZzYdxv5i7ksell5O5a5kTeyPJjZUXVBFnXlwZEyAgasFvW0yRJu4FatSrGt2i6wG0JtMc6aKBLR5kBMo5GEVFcioTkCNAfeaVLVogagiHcuJNhwG1GTGg5PX7keQ3Nd40/WnQ0MVoWZluqUfUkXUAkltD4WAfWSxDkyPKjgIv43O/zG97Ai1qqOBoayFfcWizSKpl0WvoDsYOdGf396eq4aDbmFjbV9x2C1nDXUBMSt+ba8amsLMXcMf6xb9nacTT89uE9vMAFZGAAAAAElFTkSuQmCC)
= 3.84467
108
The distance between the moon and the earth=3.84467
108 m
Question 16.Express the following information in the standard form
The charge of an electron is 0.0000000000000000016 coulombs
Answer:Given, The charge of an electron = 0.0000000000000000016 coulombs.
= 0.0000000000000000016 ![](data:image/png;base64,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)
= 1.6 ![](data:image/png;base64,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)
The charge of an electron = 1.6
coulombs.
Question 17.Express the following information in the standard form
Thickness of a piece of paper is 0.0016 cm
Answer:Given, Thickness of a piece of paper = 0.0016 cm
= 0.0016 ![](data:image/png;base64,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)
= 1.6 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACYAAAAhCAMAAACC5ikkAAAAAXNSR0IArs4c6QAAAHVQTFRFAAAAAAAAAAA6ADpmADqQAGaQAGa2OgA6OjqQOmZmOmaQOma2OpDbZgAAZgA6ZgBmZjoAZjpmZjqQZmaQZpDbZrbbZrb/kDoAkGY6kNv/tmYAtmY6ttv/tv//25A625Bm27aQ29u22////9uQ/9u2//+2///bnxkHVAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAA1UlEQVQ4T82TWxOCIBCFQY1uWnSlrLRQ+P8/seXiNJYLvtS0L8zI5zl7lllCflT6wkY41XM+BiOk+l9MlxMZj1pRqDzO9Qm1udkPrT+R/7VIDaeKZdhAi0wCFZ0lcA/O4qm0oCDoywT8KHvXw9AOrelLDo3qIoSbs0HNQMJR252Tafz57qlPlKbxN1Prq+JDmF8CkEn29v4+G8C6JaiYbKZn0zVdDJraJVDFEQaaE7WVWgSwFSiVjCiORXBqHsND9kzxx3NLUGYuAlLdEkBTySE+1+8RT96NDuxxPZAYAAAAAElFTkSuQmCC)
= 1.6 ![](data:image/png;base64,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)
Thickness of a piece of paper = 1.6
cm.
Question 18.Express the following information in the standard form
The diameter of a wire on a computer chip is 0.000005 cm
Answer:Given, diameter of a wire on a computer chip = 0.000005 cm.
= 0.000005 ![](data:image/png;base64,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)
= 5 ![](data:image/png;base64,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)
= 5 ![](data:image/png;base64,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)
The diameter of a wire on a computer chip = 5
cm.
Question 19.In a pack, there are 5 books, each of thickness 20 mm and 5 paper sheets each of thickness 0.016mm. What is the total thickness of the pack.
Answer:Given, thickness of book = 20mm
Thickness of paper = 0.016mm
The total thickness of the pack is to be found.
the total thickness of the pack = (5
20) + (5
0.016)
= 100 + 0.08
= 100.08
= 1.0008
102mm
the total thickness of the pack = 1.0008
102mm
Question 20.Rakesh solved some problems of exponents in the following way. Do you agree with the solutions? If not why? Justify your argument.
x–3 × x–2 = x–6
Answer:Given, x–3 × x–2 = x–6
the solution is wrong, because
x–3 × x–2 = x-3-2
= x-5
x–3 × x–2
x–6
Question 21.Rakesh solved some problems of exponents in the following way. Do you agree with the solutions? If not why? Justify your argument.
![](data:image/png;base64,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)
Answer:Given, ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAkAAAAYCAMAAAAfxSccAAAAAXNSR0IArs4c6QAAAEtQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOmY6Oma2OpDbZgAAZjpmZmYAZrb/kDoAkDo6kNv/tmYAtv//25A62////7Zm/9uQ//+2///bnU0dvQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAATUlEQVQYV62NSQ7AIAwDY7rRjRJoC/9/aR3UJzAHa+REskhnFBjvDJwi6qLUQGGyW9vSOy/+n8y8N8p+DMmkXrFsk4ny+wEjwLGDaQ8+JjoCjBXc6CsAAAAASUVORK5CYII=)
![](data:image/png;base64,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)
Question 22.Rakesh solved some problems of exponents in the following way. Do you agree with the solutions? If not why? Justify your argument.
![](data:image/png;base64,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)
Answer:Given, ![](data:image/png;base64,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)
(x2)3 = x2x3
= x6
the solution by Rakesh is wrong.
Question 23.Rakesh solved some problems of exponents in the following way. Do you agree with the solutions? If not why? Justify your argument.
![](data:image/png;base64,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)
Answer:Given, ![](data:image/png;base64,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)
= ![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 24.Rakesh solved some problems of exponents in the following way. Do you agree with the solutions? If not why? Justify your argument.
![](data:image/png;base64,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)
Answer:Given, ![](data:image/png;base64,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)
3
= 3![](data:image/png;base64,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)
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAhCAMAAAAieUHKAAAAAXNSR0IArs4c6QAAAGZQTFRFAAAAAAAAAAA6ADo6ADpmADqQAGa2OgAAOgA6OjoAOma2ZgA6ZpDbZrbbZrb/kDoAkDo6kGY6kLbbkLb/kNv/tmYAttv/25A625Bm27Zm27aQ2////7Zm/7aQ/9uQ/9u2//+2///b6mEI+QAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAZklEQVQoU42OSw6AIAwFHyji/4sCoij3v6SIO6MJs5k0nSYF3qiC0Bpw/QhNRdjaPPgYmlszSYKBlbc4KwHrDcXDXSzkITb/7TSnwnIGbMzI0vhOJs8bqmD3uE+uSxf/XuZm4rtvLiXaBDCIk1EBAAAAAElFTkSuQmCC)
3![](data:image/png;base64,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)
Express the following numbers in the standard form.
0.000000000947
Answer:
Given, = 0.000000000947
= 0.000000000947
= 9.47
= 9.47
0.000000000947 = 9.47
Question 2.
Express the following numbers in the standard form.
543000000000
Answer:
Given, = 543000000000
= 543000000000
= 5.43 1011
9.47
= 5.43
1011
Question 3.
Express the following numbers in the standard form.
48300000
Answer:
Given, = 48300000
= 48300000
= 4.83 107
48300000 = 4.83
107
Question 4.
Express the following numbers in the standard form.
0.00009298
Answer:
Given, = 0.00009298
= 0.00009298
= 9.28
= 9.28
0.00009298 = 9.28
Question 5.
Express the following numbers in the standard form.
0.0000529
Answer:
Given, = 0.0000529
= 0.0000529
= 5.29
0.0000529 = 5.29
Question 6.
Express the following numbers in the usual form.
4.37 × 105
Answer:
Given, = 4.37 × 105
= 4.37 100000
= 437000
4.37 × 105 = 437000.
Question 7.
Express the following numbers in the usual form.
5.8 ×107
Answer:
Given, = 5.8 ×107
= 5.8 10000000
= 58000000
5.8 ×107 = 58000000.
Question 8.
Express the following numbers in the usual form.
32.5 × 10−4
Answer:
Given, = 32.5 × 10−4
= 32.5
= 0.00325
32.5 × 10−4 = 0.00325
Question 9.
Express the following numbers in the usual form.
3.71529 × 107
Answer:
Given, = 3.71529 × 107
= 3.71529 10000000
= 37152900
3.71529 × 107 = 37152900
Question 10.
Express the following numbers in the usual form.
3789 × 10−5
Answer:
Given, = 3789 × 10−5
= 3789
= 0.03789
3789 × 10−5 = 0.03789
Question 11.
Express the following numbers in the usual form.
24.36 × 10−3
Answer:
Given, = 24.36 × 10−3
= 24.36
= 0.02436
24.36 × 10−3 = 0.02436
Question 12.
Express the following information in the standard form
Size of the bacteria is 0.0000004 m
Answer:
Given, Size of the bacteria is = 0.0000004 m
= 0.0000004
= 4
= 4
Size of the bacteria is = 4
m
Question 13.
Express the following information in the standard form
The size of red blood cells is 0.000007mm
Answer:
Given, The size of red blood cells is = 0.000007mm
= 0.000007
= 7
The size of red blood cells = 7 mm
Question 14.
Express the following information in the standard form
The speed of light is 300000000 m/sec
Answer:
Given, The speed of light is = 300000000 m/sec
= 300000000
= 3.0 108
The speed of light = 3.0
108m/sec.
Question 15.
Express the following information in the standard form
The distance between the moon and the earth is 384467000 m (app)
Answer:
Given, The distance between the moon and the earth,
= 384467000
= 3.84467 108
The distance between the moon and the earth=3.84467
108 m
Question 16.
Express the following information in the standard form
The charge of an electron is 0.0000000000000000016 coulombs
Answer:
Given, The charge of an electron = 0.0000000000000000016 coulombs.
= 0.0000000000000000016
= 1.6
The charge of an electron = 1.6
coulombs.
Question 17.
Express the following information in the standard form
Thickness of a piece of paper is 0.0016 cm
Answer:
Given, Thickness of a piece of paper = 0.0016 cm
= 0.0016
= 1.6
= 1.6
Thickness of a piece of paper = 1.6
cm.
Question 18.
Express the following information in the standard form
The diameter of a wire on a computer chip is 0.000005 cm
Answer:
Given, diameter of a wire on a computer chip = 0.000005 cm.
= 0.000005
= 5
= 5
The diameter of a wire on a computer chip = 5
cm.
Question 19.
In a pack, there are 5 books, each of thickness 20 mm and 5 paper sheets each of thickness 0.016mm. What is the total thickness of the pack.
Answer:
Given, thickness of book = 20mm
Thickness of paper = 0.016mm
The total thickness of the pack is to be found.
the total thickness of the pack = (5
20) + (5
0.016)
= 100 + 0.08
= 100.08
= 1.0008 102mm
the total thickness of the pack = 1.0008
102mm
Question 20.
Rakesh solved some problems of exponents in the following way. Do you agree with the solutions? If not why? Justify your argument.
x–3 × x–2 = x–6
Answer:
Given, x–3 × x–2 = x–6
the solution is wrong, because
x–3 × x–2 = x-3-2
= x-5
x–3 × x–2
x–6
Question 21.
Rakesh solved some problems of exponents in the following way. Do you agree with the solutions? If not why? Justify your argument.
Answer:
Given,
=
=
Question 22.
Rakesh solved some problems of exponents in the following way. Do you agree with the solutions? If not why? Justify your argument.
Answer:
Given,
(x2)3 = x2x3
= x6
the solution by Rakesh is wrong.
Question 23.
Rakesh solved some problems of exponents in the following way. Do you agree with the solutions? If not why? Justify your argument.
Answer:
Given,
=
Question 24.
Rakesh solved some problems of exponents in the following way. Do you agree with the solutions? If not why? Justify your argument.
Answer:
Given,
3
= 3
=
3