##### Class 8^{th} 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…

**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…

###### Exercise 4.1

**Question 1.**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: a^{m} × a^{n} = a(m+n)

Therefore,

=^{}2^{-15}

Answer.

**Question 7.**Simplify the following:

4^{4} ×

**Answer:**Given, = 4^{4} ×

= 4^{4}

= 5^{4}

= 625

**Question 8.**Simplify the following:

×5^{3}

**Answer:**Given, = ×5^{3}

= ^{3}

=

=

= 5^{6-1}

= 5^{5}

= 625

×5^{3} = 625.

**Question 9.**Simplify the following:

(−3)^{4} × 7^{4}

**Answer:**Given, = (−3)^{4} × 7^{4}

=

= 992401

= 194,481

(−3)^{4} × 7^{4}= 194,481

**Question 10.**Simplify

2^{2}× ×3^{-1}

**Answer:**Given, =2^{2}× ×3^{-1}

= ( )

= ^{ }( )

= 2^{4} × 3^{1}

= 16 × 3

= **48**

**2**^{2}× ×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

(4^{0} + 5^{−1}) ×5^{2} ×

**Answer:**Given, =(4^{0} + 5^{−1}) ×5^{2} ×

=(1+)5^{2}

= 5^{2}

= 25^{2-1}

= 25

= 10

(4^{0} + 5^{−1}) ×5^{2} × = 10

**Question 13.**Simplify and give reasons

**Answer:**Given, =

=

= 2^{3}4^{3}5^{3}

= 2^{3}(2^{2})^{3}5^{3}

= 2^{3}2^{6}5^{3}

= 2^{3+6}5^{3}

= 2^{9}5^{3}

= 2^{9}5^{3}

**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

×(3^{0} -3^{-1})

**Answer:**Given, = ×(3^{0} -3^{-1})

= )

=

=

=

=

×(3^{0} -3^{-1}) =

**Question 16.**Simplify and give reasons

1 + 2^{−1} + 3^{−1} + 4^{0}

**Answer:**Given, = 1 + 2^{−1} + 3^{−1} + 4^{0}

= 1 + + + 1

=

=

1 + 2^{−1} + 3^{−1} + 4^{0} =

**Question 17.**Simplify and give reasons

**Answer:**Given, =

= []^{2}

=

=

=

**Question 18.**Simplify and give reasons

**Answer:**Given, =

= [(9-4)5]^{2}

= [55]^{2}

= [5^{2}]^{2}

= 5^{4}

=625

= 625

**Question 19.**Simplify and give reasons

((5^{2})^{3} × 5^{4}) ÷ 5^{6}

**Answer:**Given, = ((5^{2})^{3} × 5^{4}) ÷ 5^{6}

= (5^{6}5^{4})

= (5^{6}5^{4}5^{-6})

= 5^{6+4-6}

= 5^{4}

= 625

((5^{2})^{3} × 5^{4}) ÷ 5^{6} = 625

**Question 20.**Find the value of ‘n’ in each of the following:

**Answer:**Given,

= (

= (

= (

Comparing powers of , we get

n2=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:

7^{2n+1} ÷ 49 = 7^{3}

**Answer:**Given, 7^{2n+1} ÷ 49 = 7^{3}

7^{2n+1} = 7^{3}

7^{2n+1} = 7^{3}

7^{2n+1} = 7^{3}

7^{2n+1-}^{2} = 7^{3}

7^{2n}^{– 1} = 7^{3}

By comparing powers of 7, we get

2n1 = 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

9m^{2} – 10n^{3}

**Answer:**Given, = 9m^{2} – 10n^{3}

Where, m = 3 and n = 2

= 93^{2}102^{3}

= (99) (108)

= 81 80

= 1

9m^{2} – 10n^{3} = 1

**Question 26.**If m = 3 and n = 2 find the value of

2m^{2} n^{2}

**Answer:**Given, = 2m^{2} n^{2}

m = 3 and n = 2

2m^{2} n^{2} = 23^{2}2^{2}

= 294

= 72

2m^{2} n^{2} = 72

**Question 27.**If m = 3 and n = 2 find the value of

2m^{3} + 3n^{2} – 5m^{2}n

**Answer:**Given, = 2m^{3} + 3n^{2} – 5m^{2}n

= 23^{3} + 32^{2} 53^{2}2

= 54 + 12 90

= 24

2m^{3} + 3n^{2} – 5m^{2}n = 24

**Question 28.**If m = 3 and n = 2 find the value of

m^{n} – n^{m}

**Answer:**Given, = m^{n} – n^{m}

= 3^{2} 2^{3}

= 9 8

= 1

m^{n} – n^{m} = 1

**Question 29.**Simplify and give reasons

**Answer:**Given, =

=

=

=

= ()^{2}

= ()^{2}

**Question 1.**

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: a^{m} × a^{n} = a(m+n)

Therefore,

=^{}2^{-15}

Answer.

**Question 7.**

Simplify the following:

4^{4} ×

**Answer:**

Given, = 4^{4} ×

= 4^{4}

= 5

^{4}

= 625

**Question 8.**

Simplify the following:

×5^{3}

**Answer:**

Given, = ×5^{3}

= ^{3}

=

=

= 5^{6-1}

= 5^{5}

= 625

×5^{3} = 625.

**Question 9.**

Simplify the following:

(−3)^{4} × 7^{4}

**Answer:**

Given, = (−3)^{4} × 7^{4}

=

= 992401

= 194,481

(−3)^{4} × 7^{4}= 194,481

**Question 10.**

Simplify

2^{2}× ×3^{-1}

**Answer:**

Given, =2^{2}× ×3^{-1}

= ( )

= ^{ }( )

= 2^{4} × 3^{1}

= 16 × 3

= **48**

**2 ^{2}× ×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

(4^{0} + 5^{−1}) ×5^{2} ×

**Answer:**

Given, =(4^{0} + 5^{−1}) ×5^{2} ×

=(1+)5^{2}

= 5^{2}

= 25^{2-1}

= 25

= 10

(4^{0} + 5^{−1}) ×5^{2} × = 10

**Question 13.**

Simplify and give reasons

**Answer:**

Given, =

=

= 2^{3}4^{3}5^{3}

= 2^{3}(2^{2})^{3}5^{3}

= 2^{3}2^{6}5^{3}

= 2^{3+6}5^{3}

= 2^{9}5^{3}

= 2^{9}5^{3}

**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

×(3^{0} -3^{-1})

**Answer:**

Given, = ×(3^{0} -3^{-1})

= )

=

=

=

=

×(3^{0} -3^{-1}) =

**Question 16.**

Simplify and give reasons

1 + 2^{−1} + 3^{−1} + 4^{0}

**Answer:**

Given, = 1 + 2^{−1} + 3^{−1} + 4^{0}

= 1 + + + 1

=

=

1 + 2^{−1} + 3^{−1} + 4^{0} =

**Question 17.**

Simplify and give reasons

**Answer:**

Given, =

= []^{2}

=

=

=

**Question 18.**

Simplify and give reasons

**Answer:**

Given, =

= [(9-4)5]^{2}

= [55]^{2}

= [5^{2}]^{2}

= 5^{4}

=625

= 625

**Question 19.**

Simplify and give reasons

((5^{2})^{3} × 5^{4}) ÷ 5^{6}

**Answer:**

Given, = ((5^{2})^{3} × 5^{4}) ÷ 5^{6}

= (5^{6}5^{4})

= (5^{6}5^{4}5^{-6})

= 5^{6+4-6}

= 5^{4}

= 625

((5^{2})^{3} × 5^{4}) ÷ 5^{6} = 625

**Question 20.**

Find the value of ‘n’ in each of the following:

**Answer:**

Given,

= (

= (

= (

Comparing powers of , we get

n2=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:

7^{2n+1} ÷ 49 = 7^{3}

**Answer:**

Given, 7^{2n+1} ÷ 49 = 7^{3}

7^{2n+1} = 7^{3}

7^{2n+1} = 7^{3}

7^{2n+1} = 7^{3}

7^{2n+1-}^{2} = 7^{3}

7^{2n}^{– 1} = 7^{3}

By comparing powers of 7, we get

2n1 = 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

9m^{2} – 10n^{3}

**Answer:**

Given, = 9m^{2} – 10n^{3}

Where, m = 3 and n = 2

= 93^{2}102^{3}

= (99) (108)

= 81 80

= 1

9m^{2} – 10n^{3} = 1

**Question 26.**

If m = 3 and n = 2 find the value of

2m^{2} n^{2}

**Answer:**

Given, = 2m^{2} n^{2}

m = 3 and n = 2

2m^{2} n^{2} = 23^{2}2^{2}

= 294

= 72

2m^{2} n^{2} = 72

**Question 27.**

If m = 3 and n = 2 find the value of

2m^{3} + 3n^{2} – 5m^{2}n

**Answer:**

Given, = 2m^{3} + 3n^{2} – 5m^{2}n

= 23^{3} + 32^{2} 53^{2}2

= 54 + 12 90

= 24

2m^{3} + 3n^{2} – 5m^{2}n = 24

**Question 28.**

If m = 3 and n = 2 find the value of

m^{n} – n^{m}

**Answer:**

Given, = m^{n} – n^{m}

= 3^{2} 2^{3}

= 9 8

= 1

m^{n} – n^{m} = 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

= 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 10^{11}

9.47 = 5.43 10^{11}

**Question 3.**Express the following numbers in the standard form.

48300000

**Answer:**Given, = 48300000

= 48300000

= 4.83 10^{7}

48300000 = 4.83 10^{7}

**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 × 10^{5}

**Answer:**Given, = 4.37 × 10^{5}

= 4.37 100000

= 437000

4.37 × 10^{5} = 437000.

**Question 7.**Express the following numbers in the usual form.

5.8 ×10^{7}

**Answer:**Given, = 5.8 ×10^{7}

= 5.8 10000000

= 58000000

5.8 ×10^{7} = 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 × 10^{7}

**Answer:**Given, = 3.71529 × 10^{7}

= 3.71529 10000000

= 37152900

3.71529 × 10^{7} = 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 10^{8}

The speed of light = 3.0 10^{8}m/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 10^{8}

The distance between the moon and the earth=3.84467 10^{8} 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 = (520) + (50.016)

= 100 + 0.08

= 100.08

= 1.0008 10^{2}mm

the total thickness of the pack = 1.0008 10^{2}mm

**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,

(x^{2})^{3} = x^{2x3}

= x^{6}

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

**Question 1.**

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 10^{11}

9.47 = 5.43 10^{11}

**Question 3.**

Express the following numbers in the standard form.

48300000

**Answer:**

Given, = 48300000

= 48300000

= 4.83 10^{7}

48300000 = 4.83 10^{7}

**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 × 10^{5}

**Answer:**

Given, = 4.37 × 10^{5}

= 4.37 100000

= 437000

4.37 × 10^{5} = 437000.

**Question 7.**

Express the following numbers in the usual form.

5.8 ×10^{7}

**Answer:**

Given, = 5.8 ×10^{7}

= 5.8 10000000

= 58000000

5.8 ×10^{7} = 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 × 10^{7}

**Answer:**

Given, = 3.71529 × 10^{7}

= 3.71529 10000000

= 37152900

3.71529 × 10^{7} = 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 10^{8}

The speed of light = 3.0 10^{8}m/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 10^{8}

The distance between the moon and the earth=3.84467 10^{8} 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 = (520) + (50.016)

= 100 + 0.08

= 100.08

= 1.0008 10^{2}mm

the total thickness of the pack = 1.0008 10^{2}mm

**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,

(x^{2})^{3} = x^{2x3}

= x^{6}

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.**

**Answer:**

Given,

3 = 3

=

3