1. Preview
Warm Up
California Standards
Lesson Presentation

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

3. California
Standards
NS2.3 Understand negative whole-number exponents. Multiply and divide expressions involving exponents with a common base.
NS2.1 Multiply, divide, and simplify rational numbers by using exponent rules.

4. The following suggests a rule for multiplying powers with the same base.
24 • 22 = (2 • 2 • 2 • 2) • (2 • 2) = 26
a3 • a2 = (a • a • a) • (a • a) = a5
Notice that the sum of the exponents in each expression equals the exponent in the answer: = 6 and = 5.

6. Additional Example 1: Multiplying Powers with the Same Base
Simplify each expression. Write your answer in exponential form.
A. 66 • 63 6
6 + 3
Add exponents. 6 9
B. n5 • n7 n
5 + 7
Add exponents. n 12

7. A. 42 • 44 4 Add exponents. 4 B. x2 • x3 x Add exponents. x
Check It Out! Example 1
Simplify each expression. Write your answer in exponential form.
A. 42 • 44 4
2 + 4
Add exponents. 4 6
B. x2 • x3 x
2 + 3
Add exponents. x 5

8. The following suggests a rule for dividing powers with the same base.3 6 32 =
= 3 • 3 • 3 • 3
= 34
3  3
3  3  3  3  3  3 1 x 5 x3 =
= x • x
= x2
x  x  x
x  x  x  x  x 1
Notice that the difference between the exponents in each expression equals the exponent in the answer: 6 – 2 = 4 and 5 – 3 = 2.

10. Additional Example 2: Dividing Powers with the Same Base
Simplify each expression. Write your answer in exponential form. 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

11. A. B. 9 9 9 Subtract exponents. 97 e e e Subtract exponents. e
Check It Out! Example 2
Simplify each expression. Write your answer in exponential form. 9 9 A. 9 2 9
9 – 2
Subtract exponents. 97 e 10 B. e 5 e
10 – 5
Subtract exponents. e 5

12. RAISING A POWER TO A POWER
To see what happens when you raise a power to a power, use the order of operations.
RAISING A POWER TO A POWER
Show the power inside the parentheses.
(c3)2 = (c ● c ● c)2
Show the power outside the parentheses.
= (c ● c ● c) ● (c ● c ● c)
= c6
Simplify.

13. RAISING A POWER TO A POWER
Reading Math
(94)5 is read as “nine to the fourth power, to the fifth power.”

14. Additional Example 3: Raising a Power to a Power
Simplify each expression. Write your answer in exponential form.
A. (54)2
(54)2
54 • 2
Multiply exponents. 58
B. (67)9
(67)9
67 • 9
Multiply exponents.
663

15. Additional Example 3: Raising a Power to a Power
Simplify each expression. Write your answer in exponential form. C.
D. (172)–20
2 3
12 • –3
Multiply exponents.
172 • –20
17–40
2 3
–36

16. A. (33)4 (33)4 33 • 4 Multiply exponents. 312 B. (48)2 (48)2 48 • 2
Check It Out! Example 3
Simplify each expression. Write your answer in exponential form.
A. (33)4
(33)4
33 • 4
Multiply exponents.
312
B. (48)2
(48)2
48 • 2
Multiply exponents.
416

17. C. D. (134)–10 Multiply exponents. Check It Out! Example 3
Simplify each expression. Write your answer in exponential form. C.
D. (134)–10
1 4
11• –2
Multiply exponents.
134 • –10
13–40
1 4
–22

18. Lesson Quiz
Simplify each expression. Write your answer in exponential form.
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 1
972
7. (9-8)9
8. (104)0 1