Name ———————————————————————
Date ————————————
Practice A
LESSON
7.1
For use with the lesson “Apply Exponent Properties Involving Products”
Name the property that is demonstrated by the example.
1. (2x)3 5 23 + x3 5 8x3
2. x4 + x5 5 x 415 5 x9
( y3)2 5 y 3+2 5 y 6
3.
Fill in the blanks.
4.
(z3)5 5 z 3
5
5z
1
7.
(24y 2)3 5 (24) ( y )
53
9. x2(x3y)2 5 x
y
(x ) y
5x
x
5x
y
y
Simplify the expression. Write your answer using exponents.
10. 82 + 85
13.
11. 52 + 54
(24)5
14.
16. (13 + 18)2
12. 7 + 78
(63)7
15.
(42)9
17. (21 + 25)5
18. (7 + 154)6
20. y2 + y 6
21. z10 + z3
Simplify the expression.
19. x3 + x
22.
(m4)7
23.
25. (3n)3
(b 9)2
24.
26. (2x)5
( p5)3
27. (xy)6
28. State Populations The table below shows the populations of selected states in 1870.
Write the order of magnitude of each of the populations.
State
Wisconsin
Nebraska
New Jersey
Oregon
Population
1,054,670
122,993
906,096
90,923
29. U.S. National Parks Hot Springs National Park in Arkansas covers an area of about
101 square miles. Kenai Fjords National Park in Arkansas covers an area that is
about 102 times the area of Hot Springs National Park. Find the approximate area of
Kenai Fjords National Park. Write your answer using exponents.
30. Mining In 2000, Canada mined approximately 104 metric tons of uranium. The
amount of metric tons of zinc mined in Canada in 2000 was approximately 102 times
this amount. About how many metric tons of zinc were mined in Canada in 2000?
7-6
Algebra 1
Chapter Resource Book
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
LESSON 7.1
y
5
(x 2y4)3 5 ( x ) ( y )
5x
x
5
6. 33 + 31 5 33
8.
+x
5. (5x)4 5 5
Answers for Chapter 7
Exponents and Exponential Functions
12. 264c21 13. 264c21 14. 625x32y 20
Lesson 7.1 Apply Exponent
Properties Involving Products
15. 2100,000a35b5 16. 250p13 17. 640m34
18. 22304x21 19. 768n17 20. 3z20
Teaching Guide
power.
2. 2 + 2 + 2 + 2 5 16
(2 + 2)(2 + 2) 5 16
The values are the same.
3. (2 + 3) + (2 + 3) +s5 216
2 + 3 + 2 + 3 + 2 + 3 5 216
The values are the same.
4. 22 + 22 + 22 5 2 + 2 + 2 + 2 + 2 + 2 5 64
2 + 2 + 2 + 2 + 2 + 2 5 64
The values are the same.
number of computers in use in Bahrain by finding
103 + 101. Then find the number of computers in
use in Australia by finding (103 + 101) + 101.
27. 104 metric tons; Solve the equation
10? + 102 5 106. 28. a. x6 cubic units
b. 15,625 cubic units c. 1,000,000 cubic units
Study Guide
1. 814 2. 64 3. y11 4. (210)8 5. 1330
6. (28)21 7. f 16 8. (w 1 8)18 9. 56 + 186
Practice Level A
10. 21331p3 11. 9x4y10 12. 8m23
1. power of a product property 2. product of
powers property 3. power of a power property
Real-Life Application
4. (z3)5 5 z3+5 5 z15
5. (5x) 5 5 x 5 625x
6. 3 + 3 5 3
4
3
1
311
4
4 4
4
53
7. (24y 2)3 5 (24)3( y2)3 5 264y6
8. (x2y4)3 5 (x2)3( y4)3 5 x6y12
9. x2(x3y)2 5 x2(x3)2y 2 5 x2x6y 2 5 x8y 2
10. 87 11. 56 12. 79 13. 220 14. 621
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
21. 32,000c13 22. 4 23. 5 24. 3 25. Answers
will vary. 26. 105 computers; First find the
15. 418 16. 132 + 182 17. 215 + 255 18. 76 + 1546
19. x4 20. y8 21. z13 22. m28 23. b18
24. p15 25. 27n3 26. 32x5 27. x6y6
28. Wisconsin: 10 6; Nebraska: 105; New Jersey:
106; Oregon: 105 29. 103 mi2
30. 106 metric tons
Practice Level B
1. 512 2. (24)10 3. (210)7 4. 87 5. 210
6. 310 7. 921 8. 158 9. (24)45 10. 134 + 194
11. 486 + 276 12. 1355 + 85 13. x7 14. y8
15. a18 16. z25 17. b14 18. (b 1 1)6
19. 81x4 20. 281x4 21. 32a5b5 22. 64x18y 6
23. 81m31 24. 36p12 25. 6 26. 3 27. 6
28. 106 newspapers 29. a. 104 tons b. 1012 t ons
c. 1018 tons 30. a. x4 square units
b. 625 square units c. 10,000 square units
Practice Level C
1. (29)14 2. 109 3. (27)8 4. 456 5. 1127
6. (26)18 7. 205 + 315 8. 1258 + 88
ANSWERS
1. a is the base, m is the exponent, and am is the
1. a. 8 + 102 b. 8 + 102 c. 104
2. a. 8 + 102 + 104 5 8 + 106 5 8,000,000
b. 8 + 102 + 8 + 102 + 104 5 82 + 108 5
6,400,000,000
Challenge Practice
1. a (x 1 9)/3 2. a12yb9y 3. xy1/2 4. x 8y 12
1
2
5. (x 1 2)5a 2 4 6. a3 cubic feet 7. } 8. }
4
3
9. (a 1 1)3 cubic feet 10. 210610 11. 220310
Lesson 7.2 Apply Exponent
Properties Involving Quotients
Teaching Guide
2+2+2
23
1. }1 5 } 5 22
2
2
2+2+2+2+2
25
2. }2 5 }} 5 23
2+2
2
4
3+3+3+3
3
}3 5 } 5 31
3+3+3
3
4+4+4+4+4+4
46
}4 5 }} 5 42
4+4+4+4
4
am
3. }n 5 am 2 n
a
Investigating Algebra Activity
1. If a is a nonzero real number and m and n are
am
positive integers with m > n, then }n 5 a m 2 n.
a
2. If a and b are real numbers with b Þ 0 and m
am
a m
.
a positive integer, then } 5 }
bm
b
1 2
9. (216)6 + 266 10. x12 11. (c 1 5)18
Algebra 1
Chapter Resource Book
A1