Evaluate the following
1) 2 
3
2) 3 
2
3) ( 2) 
4
4)  2 
4
Product of Powers Property
2
a a
3
m3  m 4
7
1) a  a
2)
8
5
f f
2
9
3
3) 5  5
3 3
4)     
4 4
2
5) x  x  x
4
3
The Product of Powers Property:
To multiply powers with the same base ________________
______________________.
7
8
6) (5m )(8m )
4 3
2 6
7) (7 x y )(4 x y )
Power of Powers Property
2 3
(n )
7 5
(c )
2 3
6 ) (5 )
3 4
7) ( x )
 3  2 
8)   
4 



4
4

9) ( 8)


6
The Power of Powers Property:
To find a power of a power _________________________ .
Power of Product Property
( 2d 4 )3
( 4m 2 )3
4 3
10) (5d )
7 2
11) ( 8d )
2 5 3
12) ( 3 x y )
8
13) (24 13)
The Power of Products Property:
_______________________________________________
_______________________________________________ .
2
7
14) ( 5) ( 5)
3 4
15) (6 )
16)
x  (3 x )
6
17)  ( 2d )
4
Name_________________________________________________________
Date __________
10.2 Practice A
Simplify the expression. Write your answer as a power.
1. 23 • 22
3.
( − 7 ) • ( −7 )
3
2. 9 6 • 98
10
5
8
5
4.  
2
 4
 4
7.  −  •  − 
 9
 9
(32 )
5
3
  1 4 
11.    
 2  


2
6. q 4 • q 4
5. c • c 5
9.
5
• 
8
8.
(4.7)3 • (4.7)2
10.
(k 5 )
12.
((9.2) )
14.
( − 2 w)5
16.
(2.5 j )3
3
10
3 6
Simplify the expression.
13.
( 4n ) 2
1 
3 
4
15.  p 
17.
(ab)18
(
18. 32 3 • 34
)
19. Is 32 • 4 2 = 12 4 ? Evaluate each side of the equation to explain
your answer.
4 3
π r and the relationship between
3
d
the radius r and the diameter d is r = .
2
20. The volume of a sphere is V =
a. Find the volume of the sphere in terms of the diameter d and simplify
the expressions.
b. What is the volume of the sphere when the diameter is
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2
centimeter?
3
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