What are the rules for exponents?

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

 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

 (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

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

 Be familiar with the following values BaseSquaresCubes

 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.)

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

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

 Radicals can be split to simplify

 Radicals CANNOT be left in the denominator

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

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

 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!