Negative and Zero Exponents

Foundations of Algebra

Zero Exponents

Anything to the zero power is equal to 1.10 =a

Is anything divided by itself equal to 1?

1114

43

3

===m

m

n

n

1114 000 mn

Simplify

1. 2x0

2. 5x3y2 0

Negative Exponents

-n n-n n

n -n

a 1 1 aa or = a

1 a a 1

A negative exponent means you move the base to the other side (opposite side) of the fraction and make the exponent positive.

Notice that the base with the negative exponent moved and became positive!

Simplify

3. x0y 4

x0 1 and y 4 1

y4

11

y4

1

y4

You can’t have negative or zero exponents in your answer.

Simplify

1.

2.

3.

4.

2s8s

5

3

s

s

2

1

s

8

1

s

Simplify

3642

8

1 yx 32

8

1yx

34

62

24

34

yx

yx.

2

3

8x

y=You can’t leave the negative exponent

There is another way of doing this without using negative exponents…

Simplify

6.a 2

a5

a 2

a5

1

a2a5

Get rid of the negative exponent.

7

1

a=

Simplify

7.p 4q 1

p3q 7

p 4q 1

p3q 7

q7

p4 p3q

Get rid of the negative exponent.

7

6

p

q=

Simplify

8.m 2n3 2

3m3 3

m 2n3 2

3m3 3 m 4n6

33 m9

m 4n6

33 m9 n6

33 m4m9

Get rid of the parenthesis.

Get rid of the negative exponents.

13

6

27m

n=

Simplify

-3x2 y 1 2

2xy3 3

9x

8y11

-9x

8y11

-9x

8y7

1.

2.

3.

4.

9x

8y7

Examples6 2

5 3

m 5

a 3b7

More Examples1

s 3

r0t 3

2 5 p0

More Examplesa9b3

ab7

(2m9n 4 )0

(3m9n 4 )3