1) Be able to evaluate powers that have zero exponents.
2) Be able to evaluate powers that have negative exponents.
3) Rewrite expressions so that exponents are positive.
4) Apply the multiplication properties of exponents to problems
involving zero exponents and negative exponents.
Product of powers property: a  a  a
m
 
Power of a power property: a
m n
n
a
m n
m n
Power of a product property:  a  b  a m  b m
m
By applying the product
of powers property to the
following example, we
find that:
3 3 3
0
7
3
3 3
0
3
7
0 7
7
3
7
3
0
3 1
7

Zero Property of Exponents
7
We can then divide
both sides of the
equation by 37 to
determine the value
of 30
A nonzero number to the zero
power is 1:
a  1, a  0
0
Evaluate the following expressions.
A.
 7
0
B. 4  4
2
2
C. 2  5
0
3
 3
D.  
 8
0
E. 00
Solutions
A. 1
B. 4  4
2
2
4
0
C. 20  5 3  1  125
1
D. 1
E. 0
0
is undefined.
 125
a a
n
By applying the product
of powers property to the
following example, we
find that:
a a
n
n
a
n  (  n)
a
1
0
We can then divide both
sides of the equation by
an to determine the value
of a-n
n
an  an
a
n
a
a
-n
n
1


1
n
a
1
an
is the reciprocal
n
of a :
a
n

1
a
,
n
a0
Evaluate the
following expressions.
2
A. 3
B.
1
4
Rewrite the following
expressions using positive
exponents.
-3
A. 5 x 4
Solutions
A. 3
B.
2
1

A. 5 x
1
32
1

9
4 3
4
4
 5

3
 64
B.
a 3
b 5


B.
1
a3
b5
a3
1
x4
5
x4
 b5
a -3
b -5
1) Evaluate the following expressions.
 3
A. -  
 5
0
B.
3
2
3
C. 9
4
9
7
 
D. 4
2 2
E.
1
32
 120
2) Rewrite the following expressions with positive
exponents.
A. y
6
B. 7c
4
C.
2s 3
r
2
D. ( 5a )
3
E.
 3x 
1 4
0
 3
A.      1
 5
B.
3
2
3
 3 2
D.
C. 9
4
 256
3
9 9
7
4  7
9
 243
3
 4 2 2
4
 3 8
 24
4
 
4
2 2
E.
1
3
2
 12  3  1
0
2
 9
A. y
6
B. 7c

4
C.
r
2
y
D.
6
c4
7
c
 5 a
3
4
 2s 3  r 2
 2s r
3 2


1
 7

2s 3
1
E.

3x

1 4
1
 5 a
3
1
125 a 3
 34  x 14

1
 x4
34
x4

81