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Copyright © by Holt, Rinehart and Winston. 67 Holt Middle School MathAll rights reserved.
Any nonzero number raised to the zero power equals 1.
x 0 � 1 with x � 0
170 � 1
Complete to see why the rules for exponents work.
1. 45 • 42 � ( ) ( ) ( ) ( )( ) • ( )( ) � 4
2. 83 • 8 � ( ) ( ) ( ) • ( ) � 8
3. 45 � 42 � �4
4
5
2� � �
4 • 44• 4
• 4• 4 • 4� � 4
4. 83 � 8 � �88
3� � �
8 • 88
• 8� � 8
5. �6
6
3
3� � 63�3 � 6 Also, �
6
6
3
3� � �
66
••
66
••
66
� � . So, 60 � .
Complete to write each product or quotient as one power.
6. 123 • 122 � 123�2 � 12 7. 94 • 93 � 9 � 9
8. �7
7
6
2� � 76�2 � 7 9. �
1
1
2
2
6
4� � 12 � 12
Write each product or quotient as one power.
10. 104 • 106 � 11. 55 • 5 � 12. 45 • 4 • 43 �
13. �1
1
5
5
6
2� � 14. �
99
5� � 15. �
2
2
1
2
0� �
Complete to evaluate each expression.
16. 2 • 50 � 2 • � 17. 6 � 80 � 6 � � 18. (5 � 1)0 � ( )0 �
Name Date Class
ReteachProperties of Exponents2-7
LESSON
To multiply powers with the same base,keep the base and add exponents.
x a • x b � x a � b
45 • 42 � 45 � 2 � 47
83 • 8 � 83 � 1 � 84
To divide powers with the same base,keep the base and subtract exponents.
x a � x b � x a � b
45 � 42 � 45 � 2 � 43
83 � 8 � 83�1 � 82
1 1 1
1 1 1
Holt Pre-Algebra
Copyright © by Holt, Rinehart and Winston. 111 Holt Middle School MathAll rights reserved.
Copyright © by Holt, Rinehart and Winston. 65 Holt Middle School MathAll rights reserved.
Practice BProperties of Exponents2-7
LESSON
25. Jefferson High School has a studentbody of 64 students. Each class hasapproximately 62 students. Howmany classes does the school have?Write the answer as one power.
62
26. Write the expression for a numberused as a factor fifteen times beingmultiplied by a number used as afactor ten times. Then, write theproduct as one power.
x 15 • x 10 � x 25
Multiply. Write the product as one power.
1. 105 • 107 2. x 9 • x 8 3. 147 • 149 4. 126 • 128
5. y12 • y 10 6. 159 • 1514 7. (�11)20 • (�11)10 8. (�a)6 • (�a)7
Divide. Write the quotient as one power.
9. �1
1
2
2
9
2� 10. �
(
(
�
�
1
1
1
1
)
)
1
8
2� 11. �
x
x
1
5
0� 12. �
1
1
6
6
1
2
0�
13. �1
1
7
7
1
2
9� 14. �
1
1
4
4
1
1
5
3� 15. �
2
2
3
3
1
9
7� 16. �
(
(
�
�
a
a
)
)
1
7
2�
Write the product or quotient as one power.
17. �2
2
2
2
8
2� 18. d 8 • d 5 19. (�15)5 • (�15)10
20. �w
w
1
3
2� 21. 3116 • 318 22. �
2
2
5
5
2
1
0
0�
23. (�x)18 • (�x)9 24. �r
r
1
7
8�
r 11(�x )27
25103124w 9
(�15)15d 13226
(�a)52381421717
168x 5(�11)4127
(�a)13(�11)301523y 22
12141416x 171012
Write the product or quotient as one power.
1. x 10 • x 8 2. (�10)14 • (�10)4 3. �dd
5� 4. 910 � 92
5. t 12 • t 5 6. �(
(
�
�
x
x
)
)
1
8
0� 7. 168 � 168 8. 149 • 149
9. (�k)12 � (�k)9 10. 15 • 1511 11. 1710 • 17 12. x 8 � x 8
Write as one power.
13. x 3 • x 2 • x 4 14. 55 � 52 • 53 15. 84 • 8 � 82
16. x 7 � x 2 � x 3 17. (�4)4 • (�4)6 � (�4)2 18. 25 � 2 • 22 � 23
19. Justine and ninety-nine of her co-workers won the lottery worth$108. They all received their winnings over ten years. How muchdid each receive in a one-year period?
$105 or $100,00020. A number to the 7th power divided by the same number to the
3rd power equals 256. What is the number?
421. The following statement is false. Make the necessary correction
to make the statement true.
To divide powers with the same base, keep the base and addthe exponents.
To divide powers with the same base, keep the base
and subtract the exponents.
23(�4)8x 2
8356x 9
x 017111512(�k)3
1418160(�x )2t 17
98d 4(�10)18x 18
Copyright © by Holt, Rinehart and Winston. 66 Holt Middle School MathAll rights reserved.
Practice CProperties of Exponents2-7
LESSON
Copyright © by Holt, Rinehart and Winston. 67 Holt Middle School MathAll rights reserved.
Any nonzero number raised to the zero power equals 1.
x 0 � 1 with x � 0
170 � 1
Complete to see why the rules for exponents work.
1. 45 • 42 � ( ) ( ) ( ) ( )( ) • ( )( ) � 4
2. 83 • 8 � ( ) ( ) ( ) • ( ) � 8
3. 45 � 42 � �4
4
5
2� � �
4 • 44• 4
• 4• 4 • 4� � 4
4. 83 � 8 � �88
3� � �
8 • 88
• 8� � 8
5. �6
6
3
3� � 63�3 � 6 Also, �
6
6
3
3� � �
66
••
66
••
66
� � . So, 60 � .
Complete to write each product or quotient as one power.
6. 123 • 122 � 123�2 � 12 7. 94 • 93 � 9 � 9
8. �7
7
6
2� � 76�2 � 7 9. �
1
1
2
2
6
4� � 12 � 12
Write each product or quotient as one power.
10. 104 • 106 � 11. 55 • 5 � 12. 45 • 4 • 43 �
13. �1
1
5
5
6
2� � 14. �
99
5� � 15. �
2
2
1
2
0� �
Complete to evaluate each expression.
16. 2 • 50 � 2 • � 17. 6 � 80 � 6 � � 18. (5 � 1)0 � ( )0 � 167121
2894154
49561010
26 � 44
74 � 35
110
2
3
48888
74444444
ReteachProperties of Exponents2-7
LESSON
To multiply powers with the same base,keep the base and add exponents.
x a • x b � x a � b
45 • 42 � 45 � 2 � 47
83 • 8 � 83 � 1 � 84
To divide powers with the same base,keep the base and subtract exponents.
x a � x b � x a � b
45 � 42 � 45 � 2 � 43
83 � 8 � 83�1 � 82
1 1 1
1 1 1
Study these patterns.
So, according to the pattern, 52 can be written as the sum of 42
and two consecutive integers.
1. Draw a diagram and write an equation to illustrate 52.
Equation:
2. Draw a diagram and write an equation to illustrate 82.
Equation:
3. Use the pattern to write an equation to indicate that, for anyinteger n, (n � 1)2 can be written as the sum of n 2 and twoconsecutive integers.
Equation:
4. If you know that 202 � 400, use the pattern to calculate 212.
212 � 400 � 20 � 21 � 441
n 2 � (n ) � (n � 1) � (n � 1)2
72 � 7 � 8 � 64 � 82
42 � 4 � 5 � 25 � 52
32 � 3 � 4 � 16 � 42
22 � 2 � 3 � 9 � 3212 � 1 � 2 � 4 � 22
1 � 12
Copyright © by Holt, Rinehart and Winston. 68 Holt Middle School MathAll rights reserved.
ChallengeSquare Dance2-7
LESSON
Holt Pre-Algebra
Holt Pre-Algebra Holt Pre-Algebra
Holt Pre-AlgebraHolt Pre-Algebra
