Course 3 • Chapter 1 Real Numbers 3

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.Lesson 2 ReteachPowers and Exponents

Example 1Write each expression using exponents. a. 7 � 7 � 7 � 7

7 � 7 � 7 � 7 = 74 The number 7 is a factor 4 times. So, 7 is the base and 4 is the exponent.

b. y � y � x � y � x

y � y � x � y � x = y � y � y � x � x Commutative Property

= (y � y � y) · (x · x) Associative Property

= y3 � x2 Defi nition of exponents

To evaluate a power, perform the repeated multiplication to fi nd the product.

Example 2

Evaluate (-6)4.

(-6)4 = (-6) � (-6) � (-6) � (-6) Write the power as a product.

= 1,296 Multiply.

The order of operations states that exponents are evaluated before multiplication, division, addition, and subtraction.

Example 3Evaluate m2 + (n - m)3 if m = -3 and n = 2.

m2 + (n - m)3 = (-3)2 + (2 - (-3))3 Replace m with -3 and n with 2.

= (-3)2 + (5)3 Perform operations inside parentheses.

= (-3 � -3) + (5 � 5 � 5) Write the powers as products.

= 9 + 125 or 134 Add.

ExercisesWrite each expression using exponents.

1. 8 � 8 � 8 � 8 � 8 2. a � a � a � a � a � a 3. 5 � 5 � 9 � 9 � 5 � 9 � 5 � 5

Evaluate each expression.

4. 24 5. (-3)5 6. (

3 −

4 )

3

ALGEBRA Evaluate each expression if a = 5 and b = -4.

7. a2 + b2 8. (a + b)2 9. a + b2

The product of repeated factors can be expressed as a power. A power consists of a base and an exponent. The exponent tells how many times the base is used as a factor.

55 � 93

a685

16 -243 27

−−

64

41 1 21

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4 Course 3 • Chapter 1 Real Numbers

NAME _____________________________________________ DATE __________________ PERIOD _________

Copyright © The M

cGraw

-Hill Com

panies, Inc. Permission is granted to reproduce for classroom

use.Lesson 2 Skills PracticePowers and Exponents

Write each expression using exponents.

1. 2 � 2 � 2 � 2 2. 9 � 9

3. 7 � 7 � 5 � 5 � 5 � 5 4. 3 −

8 � 3 −

8 �

3 −

8

5. c � 1 −

4 � c � 1 −

4 � 1 −

4 6. s � 6 � s � s � 6 � 6 � s

7. 8 � x � 2 � 2 � 2 � x � 8 8. a � (-4) � b � a � b � (-4) � (-4)

9. 1 −

3 � n � 4 � n � 1 −

3 � n � 4 � 4 10. 9 � 9 � x � w � x � y � w � 9 � y

Evaluate each expression.

11. 43 12. 25 13. (-8)3

14. (

3 −

5 )

4 15. 28 - 32 16. 23 � 52

17. 34 - (-4)2 18. 6 + 26 19. (-3)3 ÷ 32

ALGEBRA Evaluate each expression if g = 2 and h = -3.

20. g4 21. (g + h)3 22. h4 - h3

23. g3 + h2 24. (g - h)2 + h2 25. h4 - (h - g)3

9224

72 � 54 (

3 −

8 )

3

c2 (

1 −

4 )

3

s4 � 63

a2 � b2 � (-4)3x2 � 23 � 82

x2 � w2 � y2 � 93n3 � 43 � (

1 −

3 )

2

81 −−−

625 247 200

65 70 -3

16 −1 108

17 34 206

64 32 -512

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Course 3 • Chapter 1 Real Numbers 3

NAME _____________________________________________ DATE __________________ PERIOD _________

Copy

righ

t ©

The

McG

raw

-Hill

Com

pani

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nc. P

erm

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on is

gra

nted

to

repr

oduc

e fo

r cl

assr

oom

use

.Lesson 2 Homework PracticePowers and Exponents

Write each expression using exponents.

1. 3 � 3 � m 2. (

1 −

4 )

(

1 −

4 )

(

1 −

4 )

3. 2 � d � 5 � d � d � 5 4. p � (-9) � p � (-9) � p � q � q

5. g � (-7) � (-7) � g � h � (-7) � h 6. x � 1 −

8 � x � x � y � 1 −

8 � y � x

Evaluate each expression.

7. (-8)4 8. (

1 −

5 )

3 9.

(

-

3 −

5 )

5

10. (-2)3 + 52 11. 34 - 52 12. (-2)5 - (-2)4

13. 43 ÷ 23 14. 53 � 23 15. 17 + (-3)4

ALGEBRA Evaluate each expression.

16. r3 - s, if r = 5 and s = 4 17. m2 - n3, if m = 6 and n = 2

18. f - g4, if f = 3 and g = -5 19. (x5 - y2)2 + x3, if x = 2 and y = 8

20. Replace with <, >, or = to make a true statement: 24 42.

21. ISLANDS Florida has about 22 � 32 � 53 islands (over 10 acres). About how many islands is this?

32 � m (

1 −

4 )

3

2 � 52 � d3 (-9)2 � p3 � q2

(-7)3 � g2 � h2 (

1 −

8 )

2

� x4 � y2

4,096 1 −−−

125 -

243 −−−−

3,125

17 56 -48

8 1,000 82

121 28

-622

about 4,500 islands

1,032

=

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