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 exponentBase

(power

= 4 x 4 x 4 x 4 x 4 x 446

4 is a factor 6 times

The power is read “four to the sixth power.”

Algebra…

an= a x a x a x… x a

a is a factor n times

Writing powers

2 x 2 x 2 x 2 = 24

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 = 63

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 = 55

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 444

2) (-8)(-8)(-8)

(-8)3

Another example:

1) pppqqqq

=p3q4

HOWEVER,you always want the bigger exponents first…. q4p3

2) ffttffrr

=f4t2r2

Evaluate the power (write in standard form)

72 == 49

43 == 64

31 == 3

4 x 4 x 4

7 x 7

3

YOUR TURN

Write the power in words, then solve:

26 Two to the sixth power = 2 x 2 x 2 x 2 x 2 x 2 = 64

62 Six squared = 6 x 6 = 36

Evaluating Powers with Variables

Evaluate x2 when x = 9X2 = 92Substitute 9 for x

= 9 x 9

= 81

Another example…

Evaluate b3 when b = 7b3 = 73

= 7 x 7 x 7

= 343

YOUR TURN!!

Evaluate m8 when m = 2m8 = 28

= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2= 256

Another one…

Evaluate p3 when p = 10

p3 = 103

= 10 x 10 x 10

= 1000

ZERO POWER

Anything to the 0 power = 1!!

ThOuGht Of ThE dAy

• Butterflies taste with their feet.