Page 739 - Basic College Mathematics with Early Integers

A PPEND I X B . 2 I MULTIPLICATION PROPERTIES OF EXPONENTS 715

6 3
Concept Check Which property is needed to simplify 1x 2 ? Explain.
a. Product Property for Exponents
b. Power Property for Exponents
c. Power of a Product Property for Exponents

Example 7 Simplify: 15t2 3 PRACTICE 7

Simplify: 13b2 4
Solution:
15t2 = 5 t Apply the power of a product property.
3
3 3
= 125t 3 Write 5 as 125.
3
Work Practice 7

5 3 3
Example 8 Simplify: 12a b 2 PRACTICE 8
2 6 3
Simplify: 14x y 2
Solution:
5 3 3 3 5 3 3 3
12a b 2 = 2 1a 2 1b 2 Apply the power of a product property.
15 9
= 8a b Apply the power property.
Work Practice 8

4 2 4
3 5 5
Example 9 Simplify: 13y z 2 12y z 2 PRACTICE 9
2 4 4 6 9 2
Simplify: 12x y 2 13x y 2
Solution:
4 2 4 3 5 5 4 4 4 2 4 5 3 5 5 5 Apply the power of a product
13y z 2 12y z 2 = 3 1y 2 1z 2 # 2 1y 2 1z 2
property.
= 81y z 32y z Apply the power property.
15 25
16 8 #
15
#
= 181 3221y 16 # y 21z 8 # z 2
25
Group like bases.
= 2592y z
31 33
Apply the product property.
Work Practice 9

Answers
6 18
7. 81b 4 8. 64x y 9. 144x y
20 34
Concept Check Answer
b