1. Evaluate the expression.
1. x4 when x = 3
ANSWER 81
2. a2 when a = –6
ANSWER 36

2. Evaluate the expression.
3. m3 when m = –5
–125
ANSWER
4. A food storage container is in the shape of a cube. What is the volume of the container if one side is
4 inches long? Use V = s3.
ANSWER
64 in.3

3. EXAMPLE 1
Use the product of powers property
= 78 a.
73 75 = b. = =
= 911 c.
(– 5)(– 5)6
= (– 5)1 (– 5)6
= (– 5)1 + 6
= (–5)7 d.
x4 x3
= x4 + 3
= x7

4. GUIDED PRACTICE
for Example 1
Simplify the expression. 1.
32 37
= 39 2.
5 59
= 510 3.
(– 7)2(– 7)
= (–7)3 4.
x2 x6 x
= x9

5. EXAMPLE 2
Use the power of a power property a.
(25)3
= 25 3 b.
[(–6)2]5
= (–6)2 5
= 215
= (–6)10 c.
(x2)4
= x2 4 d.
[(y + 2)6]2
= (y + 2)6 2
= x8
= (y + 2)12

6. GUIDED PRACTICE
for Example 2
Simplify the expression. 5.
(42)7
= 414 6.
[(–2)4]5
= (–2)20 7.
(n3)6
= n18 8.
[(m + 1)5]4
= (m + 1)20

7. EXAMPLE 3
Use the power of a product property a.
( )8 =
(9xy)2 = (9 x y)2 = x2 y2 = 81x2y2 b.
(–4z)2 = (–4 z)2 = (–4)2 z2 = 16z2 c. d.
– (4z)2 = – (4 z)2 = – (42 z2) = –16z2

8. Use all three properties
EXAMPLE 4
Use all three properties
Simplify
(2x3)2 x4
(2x3)2 x4 = 22 (x3)2 x4
Power of a product property
= 4 x6 x4
Power of a power property
= 4x10
Product of powers property

9. EXAMPLE 5
Solve a real-world problem
BEES
In 2003 the U.S. Department of Agriculture (USDA) collected data on about 103 honeybee colonies. There are about 104 bees in an average colony during honey production season. About how many bees were in the USDA study?

10. EXAMPLE 5
Solve a real-world problem
SOLUTION
To find the total number of bees, find the product of the number of colonies, 103, and the number of bees per colony, 104.
= = 107
The USDA studied about 107, or 10,000,000, bees.
ANSWER

11. GUIDED PRACTICE
for Examples 3, 4 and 5
Simplify the expression. 9.
( )2 =
(–3n)2
10.
= 9n2
11.
(9m3n)4
= 6561m12n4
12.
5 (5x2)4
= 3125x8

12. GUIDED PRACTICE
for Examples 3, 4 and 5
13.
WHAT IF? In Example 5, 102 honeybee colonies in the study were located in Idaho. About how many bees were studied in Idaho?
about 1,000,000, bees
ANSWER

13. Daily Homework Quiz
Simplify the expression. Write your answer using exponents.
ANSWER
147
2. [(–8)4]3
ANSWER
(–8)12
Simplify the expression.
3. [(m –3)6]4
ANSWER
(m – 3)24

14. Daily Homework Quiz
4. –(2s)3
ANSWER
−8s3
A website had about 102 hits after a week. After a year, it had about 103 times the number of hits of the first week. About how many hits did it have at the end of the year ? 5.
ANSWER
About 10,000 hits