**Powers and Exponents**

A "power" is an expression written with an "exponent" and a "base" or the value of such an expression:

Power!

**3**

2

The , 3,

is the number

that is used

as the factor.

base

The ,

2, tells how many

times the base is

used as a factor.

exponent

Bell Ringer:

Bonus:

1.) (-2)(-2)(-2)

2.) (5/7)(5/7)

3.) |-40|/|8|

Evaluate each expression:

14cdf

**_**

8ce

Reading Exponents

Words

Multiplication

Power

Value

3 to the first 3 3 3

3 to the second 3 x 3 3 9

3 to the third 3 x 3 x 3 3 27

3 to the fourth 3 x 3 x 3 x 3 3 81

3 to the fifth 3 x 3 x 3 x 3 x 3 3 243

1

2

3

4

5

Evaluating Powers:

(-2)

3

-5

2

(2/3)

2

Writing Powers:

Write each number as a power of the given base:

8; base 2

8 = (2)(2)(2)

= 2

3

-125; base 5

-125 = (5)(5)(5)

= 5

3

Application:

A certain bacteria doubles every hour.

There is 1 bacterium on a slide.

If each bacterium splits (and therefore

doubles) once per hour, how many bacteria

will be on the slide after 6 hours?

Application:

We can make a diagram to "see" what's

happening each hour

Application:

After 1 hour: 2

After 3 hours: 8

After 2 hours: 4

Application:

Notice that after each hour, the number

of bacteria is a power of 2:

1 hour: 2 or 2 bacteria

2 hours: 4 or 2 bacteria

3 hours: 8 or 2 bacteria

So, after 6 hours there will be 2 bacteria

or 64 bacteria.

1

6

2

3

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

-1(5)(5) = -25

(2/3)(2/3) = 4/9