1. Properties of Exponents
Course 3
Warm Up
Problem of the Day
Lesson Presentation

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

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

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

11. RAISING A POWER TO A POWER
Reading Math
(9 ) is read as “nine to the fourth, to the fifth.” 5 4

12. 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

13. 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
2 3
–36 =
= 17–40

14. A. (33)4 (33)4 = 33 • 4 Multiply exponents. = 312 B. (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

15. = = 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
1 4
–22 =
= 13–40

16. 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