Algebra is one of the most basic part of mathematics , Algebra deals with variables and numbers.
Although Algebra is the basic mathematics , It deals with large numbers of formulas which relates two or more variables and numbers with each other.
To help you here is a list of Algebraic formulas.
Basic Algebraic Formulas:
The algebraic formulas involving basic relation between two and three variables are:
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Indices Formulas:
The formulas involving relations between variables and their powers or powers and indices are:
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![x^m \times x^n = x^{m+n} x^m \times x^n = x^{m+n}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_u5SCEGhkY50La8nLN_SBNEruJX9LDPZOdNe_do2oZiQbKN4gaosLxhVTw7GCEYX-eaUzL6TVXng7qWf5TWZ6FsmDk1SY253a7Y0gz8v4pe30xPdz1wEMOGe4gA3mqo6SlAegGMueLDupszytHQ7vpcVHC8GFxcKSexmL1S8SDXfYVYwSva28zoyJJG=s0-d)
and
![x^m \times x^n \times \ldots \times x^p = x^{m+n+ \ldots +p} x^m \times x^n \times \ldots \times x^p = x^{m+n+ \ldots +p}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_tptn1gei2IL8WdZ0A97ZcLxX3Q9nPk6gRvtL_bNB2zGq7DjnTbfrDIi83pgDEZ7mekt2hgqNQ-WJ7rcN1T3B-8ViWDKxFa-onKL_S4FUcqrJxlCDyViTwlIgN8ccNBWj3rYrkMc9VDwpS9PHFaTYYY-w716G2dKzouD3DMZziBupsra9JHDmJ840N1yzZUG1xjM9BdeWGj0E5ETqPVSH8AZ4YtrqbRGzVO_ZVcNLxIDu9_SRk5lDqdqDQnSKMq=s0-d)
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![x^m \div x^n = x^{m-n} x^m \div x^n = x^{m-n}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_tiRW5guADRfW7LC-wCkGA1Gw5F6lWkYqCbyGATVebnKggtiXOhLXiZCna2LokBJIsXuxDC27HZgqxavNZ2r5-GzB-d7BzGblv-HUC3oCjUNoKInGVCnoLoUTJD4vx62fyUblPSeGYfQ0q2xtj6YuXIsXQf-U4kXUi8dg-aWRxvz15Be5fjKQ=s0-d)
and
![x^m \div x^n \div \ldots \div x^p = x^{m-n- \ldots -p} x^m \div x^n \div \ldots \div x^p = x^{m-n- \ldots -p}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_sFwtdbpK7tNXMczZq_Tcl77tduDYpKq3-C0xUTIO18dn0Mp6NSAPtyT7HMpmgtoJO-lkGjSXEcABAwyp_E7pCYwOrdWPoVFqOamxVds9Dxqy1n7wzBWT9YmucxBnnri2FViXW4O9sCjUAeuePWynZ2Y3vrl-peRS4lcbgI3s1Yx0uePkqlGvCRMwUPYow1p7ECMcsIi0yYYaS4ijjToNzrCg-A-3-29fV6JlhFSOsBjLU=s0-d)
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![(x^m)^n = x^{m \times n} (x^m)^n = x^{m \times n}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_tcAS7VlkepsDCx9d4gO86szmcbmT8DiKsUpx41OZgI63V6HJWq8MAvy-A9GAOep6kOR5MsUrfBheZbu1SMF_40AfwJFnVlObz7_m1jlj9sEW_jlI5bXJNkJjcz3783LV2r6WjG7o1YdTkV9sdppusOnQTWfoB_sPNc8f1_8v24Br_qVPsr2Bnt=s0-d)
and
![((x^m)^n)^o) = x^{m \times n \times o} ((x^m)^n)^o) = x^{m \times n \times o}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_sZA1aRg-sivgGuJ7AENsi-I2lsLxAJC3Y4PzFsoHtPNShJcoq9O_SwaSjyV2UwPODVjr38efDQUgUCVNHo6Dy0QVZs9jNYLR3ee4Gzh207Zvjr44XZ2dhnsajmhYLVCoonE0jt6nxd3gxMXtM70hjI9n06OEpkkuWdh_iNdP8N-eSQmg04_79hAWLn_zxf6tbS0XCrAqFd9Alp=s0-d)
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![x^{-m} = \dfrac{1}{x^m} x^{-m} = \dfrac{1}{x^m}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_sV1vuDVYAZoKxLEIvjv6Ne3H1fzto1n3HYo11l5RCKf-VulCArBioG8PSpwXhr_uqLnMHpZrGZl4CCD_CM3vhmMqk6lcc2F9xn7zw0-uApE2ESHZWDkFNJB0byqgh4TtKU5vw3s-_4IHIMD47tyjG5biToD7oh87M1FoNXrQ1NHv6tDZ47e3jJNc4BHNs=s0-d)
and
![x^{m} = \dfrac{1}{x^{-m}} x^{m} = \dfrac{1}{x^{-m}}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_tELwzWkmK6W_5WEGPgBhNOP_RSoR7s-Rme8YvBA3GN7oZ7SLZyhvCC4uC4llMzPvVn3NQn4crSXdc77bb5m7iuUabhcLTtk_8orvwGG5inhE8bQ4wwP6LIIbjcpk6FF82cO1SUvH1r1W4QtI5j3xVlDQBA68xPto8h9gPzZBzQf9gvC4Aa6dwm9Y8eJt5oqD1oVw=s0-d)
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![\sqrt[m]{\dfrac{x}{y}} = \dfrac{\sqrt[m]{x}}{\sqrt[m]{y}} \sqrt[m]{\dfrac{x}{y}} = \dfrac{\sqrt[m]{x}}{\sqrt[m]{y}}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vw33nMNPstEp5TWhF7aXE-2m9-OCgU_7RYksS_cZycaIvNFrpyntF8lYYtUNjBN-018pLE5zf_C7K21lgDK6aStfuZ50qsZACsQ_2T5KvwTSxa3yd70TlJYA9zJ9D62a6TTuA24_PlSTvmXBPYSEhJYNTpcenboi2AJTUhx1rHYF6lTGeE8mPE-7NC1cn3V2IiJNrS8t923Wxs_qWWQk_FdOEmNryZvj4oyc5a-WNeuxGSSjXJOgfSusYjJChlE0x0EzEAAgcxvVfogH076Fk=s0-d)
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![\sqrt{a} \times \sqrt {b} = \sqrt{a \times b} \sqrt{a} \times \sqrt {b} = \sqrt{a \times b}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vDVH0Z_xXyl27HIWzU8Rx5Yl7UAm0nst_W4RKNPI1SSuRjdSp7FhcpoR1v9yPOaqhC3WWPqsRJKney_a4WFdQpQhCnUVpM-oMjoiIBQFDepET4OC8g74j0CyZb1Vtw17KjG7RDsSwvBKgMIS5JYwcY4_HeDAd62zCrmA-IZxBMGiSp4UzNmN7-Q9a64Ni7qq065wqj38yVQLHjYYUo13JLVtegY4t4raE=s0-d)
provided that a , b and a*b are not negative numbers.
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If,
![a^x = a^y a^x = a^y](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_ufsr5dniJuYgTmSdZvOfkP5eh41loNJ1K-JpHoAIFz8s28YG7zaKwnAriz9u9RLwgk-58J_Mdi2UCABd8ZJOvuhUzDbdvL9daWemenECgLjQgVxaMVJLOUIwF4UpDrXwFW4fU9WSm4y5a0mE-nRtu1vQ=s0-d)
then , x=y. ( Provided That :
![0 < a\text{ and }a \ne 1 0 < a\text{ and }a \ne 1](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_v2Ek7g23KbzaSmjJJlRrtNzFbfU258fJccrzOos1AkhxjgIDn2bTxbr-8VvXSObcENPj187Ki_AEZVqWrNM9TgSy4YyXqNZJrL-teE7RfBLyeJCWkafC0G-EwW71lRC6GDyT-qjJr9kVYaMiyKf-ppHW6MpIsLaEh_KnHGph9x0613NAk=s0-d)
)
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If,
![a^x = b^x a^x = b^x](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_ubZi4VINf3y2Ulk26ScGYsWTEbcf7EdhYzbftRHNbe62jcE77dlhWTgMGX3cyrGDWVTY-_FjCOawiLr3hQLBh4krSdz_0dFxQtdo-kJXGdtk8WfRs-wOskKM1qm_oz5WEH9e_-WCmCVydBUIcSUOmi_Q=s0-d)
then , a=b. ( Provided That :
![0 < a , b \text{ and }a , b \ne 1 0 < a , b \text{ and }a , b \ne 1](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_t4hMHA0Y4ubYlZl0pBKkgDkdRqAefVxTCtPyrQvJr3jC8AGpwkZD6apCqeMt0NPTomatz8DSju05sY2R_cJnXVgHBNhMj-OU_hPq6FmAFjG6incQ2SMj32WyN6DM-oovLxlPv52x6p3XNX91AAWM0JZRuNaY9VlJcqj9imhiygNy38iOCi--xDKT-fbwY=s0-d)
)