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

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

3. Learn to apply the properties of exponents.3

4. 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 4

5. 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 5

6. 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 6

7. 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 7

8. 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 8

9. 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 9

10. 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 10

11. 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 11

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

13. 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 13

14. 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 14

15. Lesson Quiz for Student Response Systems
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems 15

16. Warm-up: Homework: Page 172 #1-36 all

17. 17

18. Notice what occurs when you divide powers with the same base.
5  5  5 5 53 =
5  5  5  5  5
= 5  5
= 52 18

19. (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 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. Warm Up
1. 33 27
2. 4 • 4 • 4 • 4
256
3. b2 for b = 4 16
4. n2r for n = 3 and r = 2 18
24^8 X
81/16
• 244 6. 7. x 10 9
2 3 2 –2 21

22. Lesson Quiz for Student Response Systems
1. Write the product as one power.
d4  d3
A. d7
B. d12
C. 7d
D. 12d 22

23. Lesson Quiz for Student Response Systems
2. Write the product as one power.
44  43  42
A. 49
B. 414
C. 424
D. 4432 23

24. 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 24