8.1 Multiplication Properties of Exponents

a n = a a a…..an times Base number: the number being multiplied. a is the base number. Power: the number of times the base is multiplied. n is the power. Exponent Vocabulary

Rules for multiplying with exponents when you have the SAME BASE! PRODUCT OF POWERS PROPERTY Multiplication with the same base: a m a n = a m+n add exponents

POWER OF POWER PROPERTY Powers of powers with the same base: (a m ) n = a mn multiply exponents

Power of a Product Property Different bases, distribute power to each base and multiply. Examples: (a b) 4 = a 4 b 4 = a 4 b 4 (-3x) 2 = (-3) 2 x 2 = 9x 2

Try these! = 10,077, = 100,000,000, (2x) 3 4. [(5x) 3 ] x 3 = 8x 3 (5x) 18 = 5 18 x 18

a>1 the equation is a model for exponential growth. a<1 the equation is a model for exponential decay. Something fun to do with exponents…

Example: a x Graph 2 x 0.6 x Growth Decay

3y 2  (2y) 3 (r 2 st 3 ) 2 (s 4 t) 3 3y 2  2 3 y 3 = 3  2 3 y 5 = 24y 5 = r 4 s 2 t 6 s 12 t 3 = r 4 s 14 t 9 Some final exponent practice problems…