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Name
Class
7-5
Date
Practice
Form G
Division Properties of Exponents
Simplify each expression.
1.
56
52
2.
55
52
3.
x7
x4
4.
m 3
m 5
6.
21m8
3m 2
x6 y9
5. 2 5
x y
3
7.  
5
9.
4
4
 
7
 3x 
8.
 
 2y 
2
11.  12 p
10.



 15 p 
13.
3
4
 3 x 2 y 5 z 2 


5
 5 xz 
12.
3
3
 3x 4 
 5 
 2y 
 ab3 
 5 
a b
3
2
 4m  3n 
 2m   mn 
2
14.
3
5
3
Explain why each expression is not in simplest form.
15. 24r3
16. (3x)2
17. m3n0
18.
y5
y
Simplify each quotient. Write each answer in scientific notation.
19.
6
20. 4.5  10
5  102
3.6 107
1.5 103
Prentice Hall Gold Algebra 1 • Teaching Resources
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
43
Name
Class
7-5
Date
Practice (continued)
Form G
Division Properties of Exponents
3
 64 
21. Error Analysis A student simplifies the expression  2  as follows:
3 
3
 64 
42 3
2 3
 2   [(6  3) ]  (2 )  64. What mistake did the student make in
3 
simplifying the expression? What is the correct simplification?
22. Reasoning The division property of exponents says that to simplify powers
with the same base you subtract the exponents. Use examples to show why
powers need to have the same base in order for this technique to work.
23. The area of a triangle is 80x5 y 3. The height of the triangle is x4 y. What is the
length of the base of the triangle?
3
 12 m5 
24. Open-Ended First simplify the expression 
by raising each factor in
 15m 


the parentheses to the third power and next reducing the result. Then simplify
by some other method. Explain your method. Are the results the same? Which
method do you prefer?
Prentice Hall Gold Algebra 1 • Teaching Resources
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
44