1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

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. Problem of the Day
Calculate 6 to the fourth power minus 56.
1240

4. Learn to apply the properties of exponents.4

5. 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 5

6. 6

7. Additional Example 1: Multiplying Powers with the Same Base
Multiply. Write the product as one power.
A. 66 • 63 6
6 + 3
Add exponents. 6 9
B. n5 • n7 n
5 + 7
Add exponents. n 12 7

8. Additional Example 1: Multiplying Powers with the Same Base Continued
Multiply. Write the product as one power.
C. 25 • 2 2
5 + 1
Think: 2 = 2 1 2 6
Add exponents.
D. 244 • 244 24
4 + 4
Add exponents. 24 8 8

9. A. 42 • 44 4 Add exponents. 4 B. x2 • x3 x Add exponents. x
Check It Out: Example 1
Multiply. Write the product as one power.
A. 42 • 44 4
2 + 4
Add exponents. 4 6
B. x2 • x3 x
2 + 3
Add exponents. x 5 9

10. Cannot combine; the bases are not the same.
Check It Out: Example 1
Multiply. Write the product as one power.
C. x5 • y2
Cannot combine; the bases are not the same.
x5 • y2
D. 412 • 417 41
2 + 7
Add exponents. 41 9 10

11. Notice what occurs when you divide powers with the same base.
5  5  5 5 53 =
5  5  5  5  5
= 5  5
= 52 11

12. Additional Example 2: Dividing Powers with the Same Base
Divide. Write the quotient as one power. 7 5 3 A. 7
5 – 3
Subtract exponents. 7 2 x 10 9 B. x
10 – 9
Subtract exponents. x
Think: x = x 1 12

13. A. B. 9 9 9 Subtract exponents. 97 e e e Subtract exponents. e
Check It Out: Example 2
Divide. Write the product as one power. 9 9 A. 9 2 9
9 – 2
Subtract exponents. 97 e 10 B. e 5 e
10 – 5
Subtract exponents. e 5 13

14. (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 14

15. Additional Example 3: Raising a Power to a Power
Simplify.
A. (54)2
(54)2
54 • 2
Multiply exponents. 58
B. (67)9
(67)9
67 • 9
Multiply exponents.
663 15

16. Additional Example 3: Raising a Power to a Power
Simplify.
2 3 12 –3 C.
D. (172)–20
(172)–20
Multiply exponents.
Multiply exponents.
2 3
12 • –3
172 • –20
17–40 16

17. A. (33)4 (33)4 33 • 4 Multiply exponents. 312 B. (48)2 (48)2 48 • 2
Check It Out: Example 3
Simplify.
A. (33)4
(33)4
33 • 4
Multiply exponents.
312
B. (48)2
(48)2
48 • 2
Multiply exponents.
416 17

18. C. D. (134)–10 Multiply exponents. Multiply exponents.
Check It Out: Example 3
Simplify.
1 4 11 –2 C.
D. (134)–10
(134)–10
Multiply exponents.
Multiply exponents.
1 4
11• –2
134 • –10
13–40 18

19. Lesson Quiz for Student Response Systems
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems 19

20. 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 20

21. Lesson Quiz for Student Response Systems
1. Write the product as one power.
d4  d3
A. d7
B. d12
C. 7d
D. 12d 21

22. Lesson Quiz for Student Response Systems
2. Write the product as one power.
44  43  42
A. 49
B. 414
C. 424
D. 4432 22

23. Lesson Quiz for Student Response Systems
3. Write the product as one power.
(10–1)0
A. 10–10
B. 0
C. 1
D. 10 23