Objective- To solve problems involving negative exponents and zero exponents.

A negative exponent is an inverse!

x -1= 1

xScientific Calculator Reciprocal Key

x-1or1/xSimplify.

1)

2)

3)

4)

5)

6)

13

15

24

26

14

5

22

3

1

3

1

5

2

1

4

1

16

2

1

6

1

36

5

42

3

2

9

4

Follow the Pattern!3323130313

23

33

= 3 3 3= 3 3= 3

= 1

=1

3

=1

3

1

3

=1

3

1

3

1

3

33

3

3

3

3

Negative exponents follow rules of exponents.

Rule of Common Bases

xa

=xb xa + b

34

=3-2 34 + -2

= 32= 9

81 2

1

3

811

9= 9

Negative exponents follow rules of exponents.

Power to Power Rule

( )xa

=b

xab

( )23

=-2

23(-2)

= 2-6

= 6

1

2=

1

64

( )8-2

= 2

1

8=

1

64

Simplify.1)

2)

3)

4 25 5

2 1(8 )

2 3 5(7 ) 7

4)

5)

6)

2 43 3 3

3 22 5

3 2(4 4)

4 25

25 25

2( 1)8

28 1

64

6 57 7 17 1

7

2 4 13

13 1 3

18

25

8

25

3 1 2(4 )

2( 2)4 44 256

6 4

4 a b

2

3

m

Simplify.1)

2)

3)

23m

26xy

2(6xy)

4)

5)

6)

4 4y y

3 3(2xy )

3 2 4(2a ) (b)

2

13

m

2

16x

y

2

6x

y

2

1

(6xy) 2 2

1 36x y

44

1y

y 1

3 3

1

(2xy ) 3 9

1 8x y

2

3 4

2 1

a b

Simplify.03 Factor

ExplanationNegative Exponent

Explanation43 3 3 3 3 33 3 3 3 23 3 313 303 1

11

11

32

=3-2

32 + -2

= 30= 1

9 2

1

3

91

9= 1

1

For all real numbers x, except x = 0, 0x 1

Negative Exponents in Denominator

Evaluate.

2

3

x 23 x 2

3 1

1 x

23 x

1 1 23x

2

3

x 23x

Simplify.

1)

2)

3)

4)

4

1

3

3

x

y

2

1

5a

3 4

m

7x y

43 81

3xy

25a 225a

3 4mx y

7