1. Learn to apply the properties of exponents.

3. 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

4. Cannot combine; the bases are not the same.
Example 2
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

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

6. Example 3: 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

7. A. B. 9 9 9 Subtract exponents. 97 e e e Subtract exponents. e
Example 4
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

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

9. Example 5: 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

10. A. (33)4 (33)4 = 33 • 4 Multiply exponents. = 312 B. (48)2 (48)2
Example 6
Simplify.
A. (33)4
(33)4
= 33 • 4
Multiply exponents.
= 312
B. (48)2
(48)2
= 48 • 2
Multiply exponents.
= 416

11. = = C. D. (134) –10 Multiply exponents. Multiply exponents. Example 7
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

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