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What are the rules for exponents?

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x n Base: the number to be multiplied by itself Exponent: how many times the base is to multiplied by itself => EXPONENT => BASE

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Always step down one step from the base operation for the rule for the exponent Exponent and Roots Multiplication and Division Addition and Subtraction No Step below addition and subtraction that’s why the exponents must be the same

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(2 3 ) 4 = 2 12 Exponent use multiplication (2 3 )(2 4 ) =2 3+4 =2 7 Multiplying use addition x 2 + 2x 2 3x 2 Addition like terms only x 2 – 2x 2 = – x 2 roots use division Division use subtraction Subtraction, like terms only X 0 =1 ∀ x ≠0 Special rule

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x -n = 1. x n And A negative exponent means the items belongs on the other side of the fraction bar

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Be familiar with the following values BaseSquaresCubes 000 121 248 3927 41664 525125 636216 749 864 981 10100

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Simplifying Square roots use a factor tree and remove groups of 2 (if you are working with cube roots, remove in groups of 3, etc.) 3 25 5 5

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The same number must be under the radical in order to add or subtract

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Radicals must have the same index in order to multiply or divide

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Radicals can be split to simplify

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Radicals CANNOT be left in the denominator

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log b N = x => N = b x Used when N is a power of b

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log(N) = x log(b) Used when N is NOT a power of b OR

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log 2 16 = x 16 = 2 x 2 4 = 2 x 4 = x When the bases are equal the Exponents are equal log 3 8 log(8) = 1.89 log(3) Make sure you close the parentheses 10 x = 3 log 10 x = log 3 x log 10 = log 3 x = log(3) log(10) x =.477 Always follow the basic principle of equations---whatever you do to one side do to the other!

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