1. 1

2. Warm Up Evaluate. 1. 33 27 2. 4 • 4 • 4 • 4 256 3. b2 for b = 4 16
4. n2r for n = 3 and r = 2 18 2

3. The factors of a power, such as 74, can be grouped in different ways
The factors of a power, such as 74, can be grouped in different ways. Notice the relationship of the exponents in each product.
7 • 7 • 7 • 7 = 74
(7 • 7 • 7) • 7 = 73 • 71 = 74
(7 • 7) • (7 • 7) = 72 • 72 = 74 3

4. 4

5. Example 1: Multiplying Powers with the Same Base
Multiply. Write the product as one power.
B. n5 • n7
A. 66 • 63 n
5 + 7 6
6 + 3 n 12 6 9
C. 25 • 2
D. 244 • 244 2
5 + 1 24
4 + 4 2 6 24 8 5

6. A. 42 • 44 4 4 B. x2 • x3 x 41 x 41 Check It Out: Example 1
Multiply. Write the product as one power.
A. 42 • 44
C. x5 • y2 4
2 + 4
x5 • y2 4 6
B. x2 • x3
D. 412 • 417 x
2 + 3 41
2 + 7 x 5 41 9 6

7. Notice what occurs when you divide powers with the same base.
5  5  5 5 53 =
5  5  5  5  5
= 5  5
= 52 7

8. Example 2: Dividing Powers with the Same Base
Divide. Write the quotient as one power. 7 5 3 A. x 10 9 B. 7
5 – 3 x
10 – 9 7 2 x 8

9. A. B. 9 e 9 e 9 e 97 e Check It Out: Example 2
Divide. Write the product as one power. 9 9 e 10 A. B. 9 2 e 5 9
9 – 2 e
10 – 5 97 e 5 9

10. (9 ) is read as “nine to the fourth, to the fifth.”
Reading Math
(9 ) is read as “nine to the fourth, to the fifth.” 5 4 10

11. Example 3: Raising a Power to a Power
Simplify.
A. (54)2
B. (67)9
(54)2
(67)9
54 • 2
67 • 9 58
663
2 3 12 –3 C.
D. (172)–20
(172)–20
2 3
12 • –3
172 • –20
17–40 11

12. Lesson Quiz
Write the product or quotient as one power.
1. n3  n4 n 7
2. 8 • 88 8 9 t9 t7
109
105 3. 4. 10 4 t 2
5. 32 • 33 • 35 3 10
6. (m2)19
m38
7. (9-8)9
8. (104)0 1
9–72 12