Powers and Exponents

Objective You will be able to write repeated multiplication using exponents. Word Watch: -power -base -exponent

Vocab A power is a way of writing repeated multiplication. The base of a power is the factor. The exponent of a power is the number of times the factor is used.

4 6  exponent Base  ( power = 4 x 4 x 4 x 4 x 4 x is a factor 6 times   The power is read “four to the sixth power.”

Algebra… anan = a x a x a x… x a a is a factor n times  

Writing powers 2 x 2 x 2 x 2 = is a factor 4 times This is read “two to the fourth power.”

Example 6 x 6 x 6 = ?? 6 x 6 x 6 = 6 3 This is read, “six cubed.”

YOUR TURN 5 x 5 x 5 x 5 x 5 = ?? 5 x 5 x 5 x 5 x 5 = 5 5 How is this read?? “five to the fifth power”

GO THE OTHER WAY!! Write each expanded form in exponent form. 1) 4 x 4 x 4 x 44 2) (-8)(-8)(-8) (-8) 3

Another example: 1) pppqqqq =p 3 q 4 HOWEVER,you always want the bigger exponents first…. q 4 p 3 2) ffttffrr =f 4 t 2 r 2

Evaluate the power (write in standard form) 7 2 = = = = = = 3 4 x 4 x 4 7 x 7 3

YOUR TURN Write the power in words, then solve: 2626 Two to the sixth power = 2 x 2 x 2 x 2 x 2 x 2 = Six squared = 6 x 6 = 36

Evaluating Powers with Variables Evaluate x 2 when x = 9 X 2 = 9 2 Substitute 9 for x = 9 x 9 = 81

Another example… Evaluate b 3 when b = 7 b 3 = 7 3 = 7 x 7 x 7 = 343

YOUR TURN!! Evaluate m 8 when m = 2 m 8 = 2 8 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 256

Another one… Evaluate p 3 when p = 10 p 3 = 10 3 = 10 x 10 x 10 = 1000

ZERO POWER Anything to the 0 power = 1!!

ThOuGht Of ThE dAy Butterflies taste with their feet.