Algebra 1 Section 8.2

Properties of Exponents Quotient Property: = xa-b xa xb Negative exponent: x-a = 1 xa

Example 2 Simplify . 24x2y6z7 -8xy2z5 -3 x2-1 y6-2 z7-5 -3xy4z2

Properties of Exponents Since x-a = , we also know 1 xa that = xa. 1 x-a a-2 = 1 a2 = 52 1 5-2

Example 3 1 x4 y2 = y2 x4 a. x-4y2 = 1 x2 2( ) = 2 x2 b. 2x-2 =

Example 3 c. (-3x-2)3 = (-3)3x-2(3) = -27x-6 = 1 x6 -27( ) = 27 x6

Example 3 d. ( x-3)-2 = 1 3 ( )-2x-3(-2) = 1 3 32x6 = 9x6

Properties of Exponents Quotient Property: = xa-b xa xb Negative exponent: x-a = 1 xa Zero exponent: x0 = 1

Example 4 Divide and express the answer in positive exponential form. 34x-3y2z-5 -18x-6y2z-2 34 18 x-3-(-6) y2-2 z-5-(-2) 17 9 = 17x3 9z3 = 17x3(1) 9z3 x3 y0 z-3

Properties of Exponents The power of a quotient is equal to the quotient of the powers: a b = an bn n ( )

( ) Example 5 Simplify, leaving all variables in the numerator: y x2 (x3y-4)2 3 ( ) x6-6y3+(-8) x0y-5 y3 x6 (x6y-8) y-5

Properties of Exponents An expression containing negative exponents in the denominator is not considered to be simplified. It is generally preferable to use only positive exponents in a simplified expression.

Homework: pp. 336-337