Multiplication and Division Properties of Exponents Exponent Vocabulary

Multiplication and Division Properties of Exponents

Exponent Vocabulary an = 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.

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

POWER OF POWER PROPERTY Powers of powers with the same base: m n (a ) 4 3 (z ) = = mn a 12 z 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 (-3 x)2 = (-3) 2 • x 2 = 9 x 2

Rules for Division QUOTIENT OF POWERS PROPERTY Division with the same base m a = am-n Subtract exponents 13 g = g 10 Subtract exponents n a 3 g

Rules for Division Power of Quotient Property Distribute power across the ( ) m a = m b b w k 4 3 2 x x 4 w = 4 k 6 x = 2 x 3 x =

Try these! Simplify: 1. 69 = 5 4 66 10, 077, 696 3. (2 x)3 23 x 3 = 2. 2 9 10 10 1011 = 100, 000, 000 4. [(5 x)3]6 8 x 3 (5 x)18 = 5 18 x 18

Practice 1. 37 34 = 33 2 8 8 2. 85 3. 2 3 = 27 = 83 = 8 -2 = 1 82 85 2 = 22 32 =4 9 =1 64

Some final exponent practice problems… 3 y 2 (2 y)3 3 y 2 23 y 3 =3 23 y 5 =24 y 5 (r 2 st 3)2(s 4 t)3 = r 4 s 2 t 6 s 12 t 3 = r 4 s 14 t 9

Try the Challenge Problem 16 x 3 y ∙ -2 xy Multiply straight across to make one fraction. 3 -4 xy -x -32 x 4 y 2 Divide whole numbers 2 3 4 x y exponents and -8 x 4 y 2 Subtract 2 make sure all exponents in -8 x x 2 y 3 your answer are positive. y