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
es, I
nc. P
erm
issi
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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