This document provides instruction on exponents and properties of exponents, including: 1) Multiplying powers with the same base by keeping the base and adding the exponents. 2) Dividing powers with the same base by keeping the base and subtracting the exponents. 3) Raising a power to a power by multiplying the exponents. Examples are provided and students complete practice problems applying these properties of exponents. A brief quiz at the end reviews key concepts from the lesson. The assignment is to complete problems 1-36 applying exponent properties.

1. 3-2 Before the Bell
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. 3-2
Today’s learning
Target:
I can apply the properties of
exponents.

3. 3-2
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. 3-2 Vocabulary
Multiplying Powers with the SAME base
Words Numbers Algebra
Keep the base 35 3 8 bm b n
and add the 35+8 = bm+n
exponents 313

5. 3-2 I’ll show you.
Multiply. Write the product as one power.
A. 66 • 63
66 + 3 Add exponents.
69
B. n5 • n7
n5 + 7 Add exponents.
n 12

6. 3-2 You try it with a partner!
Multiply. Write the product as one power.
C. 25 • 2
25 + 1 Think: 2 = 2 1
26 Add exponents.
D. 244 • 244
24 4 + 4 Add exponents.
24 8

7. 3-2 Try it by yourself.
Multiply. Write the product as one power.
1. 42 • 44
42 + 4 Add exponents.
46

8. 3-2
Notice what occurs when you divide powers
with the same base.
55 5• 5• 5• 5• 5
= = 5 • 5 = 52
53 5• 5• 5

9. 3-2 Vocabulary
Dividing Powers with the SAME base
Words Numbers Algebra
Keep the base 38 = 38-2 = 36 bm = bm-n
and subtract the 32 bn
exponents

10. 3-2 I show you one, then you do one:
Divide. Write the quotient as one power.
5
A. 7
3
7
75 – 3 Subtract exponents.
2
7
10
B. x9
x
x10 – 9 Subtract exponents.
x Think: x1 = x

11. 3-2 Try this one by yourself:
Divide. Write the product as one power.
99
2.
92
99 – 2 Subtract exponents.
97

12. 3-2 Vocabulary
Raising a Power to a Power

13. 3-2 I show you one, then you do one:
Simplify.
A. (54)2
(54)2
54 • 2 Multiply exponents.
58
B. (67)9
(67)9
67 • 9 Multiply exponents.
663

14. 3-2 I show you one, then you do one:
Simplify.
12 –3
C. 2 D. (172)–20
3
(172)–20
Multiply exponents.
Multiply exponents.
2 12 • –3
172 • –20
3
17–40

15. 3-2 Did you master today’s learning target?
Prove it with a three
question quiz.

16. 3-2 Lesson Quiz
Write the product or quotient as one power.
1. n3 × n4 n7 2. 8 • 88 89
109 t9
3. 104 4. t2
105 t7
5. 32 • 33 • 35 310 6. (m2)19 m38
7. (9-8)9 9–72 8. (104)0 1

17. Answers to lesson 3-1

18. 3-2 Assignment:
Section 3-2
Problems 1 – 36 all