Chapter4.3

Evaluating Algebraic Expressions

4-3 Properties of Exponents

Warm Up

California StandardsCalifornia Standards

Lesson Presentation

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Warm UpEvaluate.

271. 33

2. 4 • 4 • 4 • 4

3. b2 for b = 4

4. n2r for n = 3 and r = 2

256

16

18



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.



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: 4 + 2 = 6 and 3 + 2 = 5.



Additional Example 1: Multiplying Powers with the Same Base

A. 66 • 63

69

66 + 3

B. n5 • n7

n12

n5 + 7

Add exponents.

Add exponents.

Simplify each expression. Write your answer in exponential form.



Check It Out! Example 1

A. 42 • 44

46

42 + 4

B. x2 • x3

x5

x2 + 3

Add exponents.

Add exponents.




The following suggests a rule for dividing powers with the same base.

Notice that the difference between the exponents in each expression equals the exponent in the answer: 6 – 2 = 4 and 5 – 3 = 2.

36

32= = 3 • 3 • 3 • 3 = 34

3 33 3 3 3 3 31 1

1 1

x5

x3= = x • x = x2

x x xx x x x x1 1 1

1 1 1



Subtract exponents.

72

75 – 3

75

73

Additional Example 2: Dividing Powers with the Same Base


A.

x10

x9B.

Subtract exponents.x10 – 9

x Think: x = x1



Subtract exponents.

97

99 – 2

99

92


A.

B. e10

e5

Subtract exponents.e10 – 5

e5




RAISING A POWER TO A POWER

To see what happens when you raise a power to a power, use the order of operations.

(c3)2 = (c ● c ● c)2

= (c ● c ● c) ● (c ● c ● c)

= c6

Show the power inside the parentheses.

Show the power outside the parentheses.

Simplify.



RAISING A POWER TO A POWER

Reading Math

(94)5 is read as “nine to the fourth power, to the fifth power.”




Multiply exponents.

Additional Example 3: Raising a Power to a Power

A. (54)2

(54)2

54 • 2

58 B. (67)9

(67)9

67 • 9

663

Multiply exponents.



Multiply exponents.

Additional Example 3: Raising a Power to a Power

C. D. (172)–20

172 • –20

17–40

2 3

12 • –3


2 3

–36



Multiply exponents.


A. (33)4

(33)4

33 • 4

312 B. (48)2

(48)2

48 • 2

416

Multiply exponents.




Multiply exponents.


C. D. (134)–10

134 • –10

13–40

1 4

11• –2


1 4

–22



Lesson Quiz

3.

8 9n 71. n3 n4

109

105 10 4 4.

t 2

5. 32 • 33 • 35 3 10

2. 8 • 88

t9

t7

6. (m2)19 m38

7. (9-8)9 8. (104)0 1


1972

Chapter4.3

Technology

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