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

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

EXAMPLE 1 Use the product of powers property = 78 a. 73 75 = 73 + 5 b. 9 98 92 = 91 98 92 = 91 + 8 + 2 = 911 c. (– 5)(– 5)6 = (– 5)1 (– 5)6 = (– 5)1 + 6 = (–5)7 d. x4 x3 = x4 + 3 = x7

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

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

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

EXAMPLE 3 Use the power of a product property a. (24 13)8 = 248 138 (9xy)2 = (9 x y)2 = 92 x2 y2 = 81x2y2 b. (–4z)2 = (–4 z)2 = (–4)2 z2 = 16z2 c. d. – (4z)2 = – (4 z)2 = – (42 z2) = –16z2

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

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?

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. 103 104 = 103+4 = 107 The USDA studied about 107, or 10,000,000, bees. ANSWER

GUIDED PRACTICE for Examples 3, 4 and 5 Simplify the expression. 9. (42 12)2 = 422 122 (–3n)2 10. = 9n2 11. (9m3n)4 = 6561m12n4 12. 5 (5x2)4 = 3125x8

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

Daily Homework Quiz Simplify the expression. Write your answer using exponents. 145 142 ANSWER 147 2. [(–8)4]3 ANSWER (–8)12 Simplify the expression. 3. [(m –3)6]4 ANSWER (m – 3)24

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