6.1 Properties of Exponents Use properties of exponents Use negative and zero as an exponent EQ: What are the general rules involving properties of exponents? Objective 4 2 Base Exponent

Product of Powers Property To multiply powers having the same base, add the exponents. a m a n = a m + n Example: = = 3 9 Power of a Power Property To find a power of a power, multiply the exponents. (a m ) n = a m n Example: (5 2 ) 4 = 5 24 = 5 8 Power of a Product Property To find a power of a product, find the power of each factor and multiply. (a b) m = a m b m Example: (2 3) 6 = Multiplication Properties

y y (-5) (-5) 4 1.

x 32 x6x6 (-2) 34 (-2) 12 (a – 2) 32 (a – 2)

x4y434x4y4 (-3) 2 y 2 9y 2 – 3 2 y 2 –9y 2 81x 4 y

3 2 (x 4 ) 2 y 2 y x 42 y 2 y 5 9 x 8 y 2+5 9x 8 y 7 2.

Division properties of exponents. Quotient of Powers Property To divide powers having the same base, subtract the exponents Example: Power of Quotient property To find the power of a quotient, find the power of the numerator and the power of the denominator and simplify. Example

DEFINITION OF ZERO AND NEGATIVE EXPONENTS Let a be a nonzero number and let n be a positive integer. A nonzero number to the zero power is 1: a 0 = 1, a ≠ 0 a –n is the reciprocal of a n : a –n = 1, a ≠ 0 a n

y14y d.= = = e. = Undefined.

4 – –2– ,