8.1-8.3 The Rules of Exponents Algebra 8.1-8.3 The Rules of Exponents

Exponent Table Property Meaning Example Product of Powers Property Power of a Power Property Power of a Product Property

Definitions EXPONENT 5 3 BASE

Examples Using Product of Powers Let’s try three together! . 1) x x = 2 4 6 x . . 2) y y y = 3 4 y 8 . 3) x y xy = 3 2 5 4 7 x y Try these two on your own! . 8 4) 3 3 = 7 3 8 5) (-6) (-6) = 4 4 (-6)

Examples Using Power of a Power 1) (9 ) = 3 4 12 9 3 2 6 2) [(-3) ] = (-3) Let’s try two together! Try this one on your own! 3) (x ) = 2 4 x 8

Examples Using Power of a Product Let’s try two together! 1) (x y ) = 3 2 3 9 6 x y 2) -(2y ) = 3 4 -16y 12 Try these two on your own! 4) (-2y ) = 3 4 12 16y 3 1 1 2 6 3) [ a b ] = 3 9 a b 27 3

Using All Three Properties Together Let’s try one together! . 3 5 2 3 1) (5x y ) x = 11 9 125x y Try this one on your own! 2 3 16 8 2) (3a b) (2a b ) = 2 4 2 72a b

Exponent Table Property Meaning Example Product of Powers Property Power of a Power Property Power of a Product Property Zero as an Exponent Why? See table. Why? See table. Negative Exponents Dividing with Exponents Power of a Quotient Property Move any exponent across the fraction bar to change the sign of the exponent.

[ ] Examples 1) = 3 2) = 8a b 2a b 3) a b 4b 1 1 3 = = 27 3 3 1) = -3 = 3 = 3 27 5 3 3 Let’s try two together! -2 2 [ ] 3 -2 3 4 16 2) = = -2 2 3 9 4 4 Try this one on your own! 8a b 2a b 3 -1 8 4 7 3) = 4a b a b 4b -2 4 -2

HW P. 804 #1-28