Division with Exponents & Negative and Zero Exponents

Essential Questions

How do I use the division properties of exponents to evaluate powers and simplify expressions?

How do I evaluate powers that have negative and zero exponents?

Activator

Simplify1. (3w2)2

2. (4vw3)2

3. (2xy3)4(4x2y5) Solutions:

1. 9w4

2. 16v2w6

3. 64x6y17

Quotient of Powers Property To divide powers having the same

base, subtract exponents.

m

m-nn

a= a , a 0

a

Example: 77-5 2

5

3= 3 = 3

3

Power of a Quotient Property To find the power of a quotient, find

the power of the numerator and the power of the denominator and then divide.

m m

m

a a= , b 0

b b

Example:

3 3

3

4 4=

5 5

Example 1 Simplify

completely.6

6

5

4 1. 2.

= 61

= 6

4

4

5

3

= 42

= 16

Example 2 Simplify completely.

22

3

1. 2. 33

y

2

2

2

3

4

9

3

3

( 3)

y

3

27

y

Zero Exponents A nonzero number to the zero power is 1!

a0 = 1, a≠0

Example: 50 = 1

Hmmm…why is that true? Look at the following example:

41

4

1

1

4That is the same as

4When we subtract exponents we get 40!

So 40 = 1

Negative Exponents

Negative exponents must be moved to the denominator!

This makes them positive!!

Example:-2

2

1 13 = =

3 9

Example 3

Simplify

1. (-2)0

= 1

-x52.

x

1

5

Example 4

Simplify 2 2

4

2x y 9xy•

3x y3 3

4

18x y=

3xy2 -1= 6x y

2

=6x

y

Try This! Simplify

3 2 2

3

3x y 12x y•

4x y

5 3

3

36x y=

4xy4 0= 9x y

4= 9x