1. No category

Name———————————————————————— Lesson
2.1
Date —————————————
Practice B
For use with the lesson “Use Properties of Exponents”
Evaluate the expression. Tell which properties of exponents you used.
1. 25 p 23
2. (27)2(27)
3. 426 p 421
4.
(522)2
5.​ }
  ​
23
824
6.​ }
  ​
82
7.​1 }
​ 3 ​ 2​ 4 23
8.​ }
​ 5 ​  ​
427
4
1  2
2 3
Write the answer in scientific notation.
10. (2.6 3 1027)(1.3 3 102)
11.
(3.4 3 1021)(3.1 3 1022)
12. (5.8 3 1027)(8.1 3 1012) 13. (4.5 3 104)2
14.
(3.7 3 1025)2
15. (7.2 3 1023)3
9.9 3 109
16.​ }8 
 ​
1.5 3 10
8.4 3 1026
17.​ } 
  
​
2.4 3 109
Lesson 2.1
9. (6.1 3 105)(2.2 3 106)
Simplify the expression. Tell which properties of exponents you used.
18.​ }4 ​
y4
19.​ } 
  ​
y27
21. (40w 2)25
22.
24. (7c7d 2)22
25. (5g 4h23)23
x 5y28
26.​ }
 
 ​
x 5y26
12a23b 9
28.​ }
 
 ​
21a 2b25
8e24f 22
29.​ } 
  
​
18ef 25
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
x8
x
16q0r26
27.​ }
 
 ​ 
23 27
4q r
( y 4z 2)( y 23z25)
20.
(32s 3)6
23.
(2m3n21)(8m 4n22)
Write an expression for the surface area or volume in terms of x.
1
31. V 5 ​ } ​ π r 2h
3
30. S 5 4πr 2
x
3
4
32. V = ​ } ​ π r 3
3
x2
2x 2
2x
33. Birds Some scientists estimate that there are about 8600 species of birds in the
world. The mean number of birds per species is approximately 12,000,000. About
how many birds are there in the world? Write your answer in scientific notation.
34. Biology A red blood cell has a diameter of approximately 0.00075 centimeter. If
one of the arteries in your body has a diameter of 0.0456 centimeter, how many red
blood cells could fit across the artery? Write your answer in scientific notation.
Algebra 2
Chapter Resource Book
2-7
Answers for Chapter 2
Lesson 2.1 Use Properties of
Exponents
1
17. 23125 18. ​ } ​ 19. 6561 20. 32
8
Teaching Guide
24. 5.983 3 1012 25. 1.76 3 1016
1. 22: 3 2. 81; 9; 729; 729 3. 25; 125; 3125;
3125 4. It is equivalent to the base raised to the
sum of the two exponents. 5. A way to write
26. 7.0 3 1027 27. 4.8 3 109 28. 3.534 3 103
Investigating Algebra Activity
1. a. (6 p 6 p 6 p 6)(6 p 6 p 6 p 6 p 6 p 6 p 6); 611
b. (3 p 3 p 3 p 3)(3 p 3 p 3 p 3)(3 p 3 p 3 p 3); 312
5p5p5p5p5p5p5p5
c. }}
​ 
  
    ​5 5 p 5 p 5 p 5; 54
5p5p5p5
4p4p4p4p4 4
4 4 4 4 4
d. ​ } ​p }
​   ​p }
​   ​p }
​   ​p }
​   ​5 }}
​ 7 p 7 p 7 p   
 ​; }
​   ​
7 p 7 75
7 7 7 7 7
2. See answers to Exercise 1. 3. For the product
5
21. 5.27 3 105 22. 5.26 3 1025 23. 2.3 3 1023
29. 7.84 3 106 30. 1.849 3 105 31. 6.0 3 102
32. 7.5 3 101 33–40. Check properties.
33. b6 34. x 2 35. s14 36. 25y 2 37. z 4
16
x3
1
38. }
​  4    ​ 39. ​ }
 ​  40. }
​  2  ​ 41. 3.26 3 108
27
m
n
4
42. about 2.65 3 10 dollars
Practice Level B
1– 8. Check properties. 1. 256 2. 2343
8
1
1
1
1
   ​ 4. }
​ 625   ​  5. ​ }
   ​  6. ​ }
   ​ 7. }
​ 27  ​ 
3. ​ }
16,384
256
262,144
125
8. ​ }  ​ 9. 1.342 3 1012 10. 3.38 3 1025
64
of powers property, the exponents in the
Simplified form column are the sum of the
exponents in the Exponential expression column.
For the power of a power property, the exponents
in the Simplified form column are the product
of the exponents in the Exponential expression
column. For the quotient of powers property, the
exponents in the Simplified form column are the
difference of the exponents in the Exponential
expression column. For the power of a quotient
property, the exponent in the Exponential
expression column is applied to the numerator
and denominator to give the expression in the
Simplified form column. 4. Sample answer:
The product of powers property means that if you
are multiplying like bases, the exponents will be
added. The power of a power property means
that if you are raising a power to a power, the
exponents will be multiplied. The quotient of a
power property means that if you are dividing like
bases, the exponents will be subtracted. The power
of a quotient property means that if you are
raising a quotient to a power, you will raise both
the numerator and denominator to that power.
11. 1.054 3 1022 12. 4.698 3 106
Practice Level A
2m7
45c13
9
27r 6
}
}
}
16. 2​ }
 
 
​
17.
​ 
 
 
 
​
18.
1
19.
​ 
 
 
 
​
20.
​ 
  
​
n6
d5
x 14y 2
q 3s 3
1
21. ​ }
   ​ 22. b 18 23. Sample answer: a 4b 4c 5
z12
24. Sample answer: 6x 3y 4z 25. Sample answer:
1
1. 9 2. 125 3. 32 4. 256 5. 1 6. ​ } ​
2
1
1
7. }
​ 49  ​ 8. }
​ 1,000,000
   ​ 
9–20. Check properties.
9. 1024 10. 2243 11. 15,625 12. 1
25
1
13. }
​ 32  ​ 14. 27 15. 1,000,000,000 16. }
​ 36 ​ 
answers
numbers using powers of 10 having the form
c 3 10n where 1 ≤ c < 10 and n is an integer;
6.4 3 107; 3.4 3 1024
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
Polynomials and Polynomial Functions
13. 2.025 3 109 14. 1.369 3 1029
15. 3.73248 3 1027 16. 6.6 3 101
17. 3.5 3 10215 18–29. Check properties.
18. x 4 19. y 11 20. 531,441s18
y
16m7
1
1
}
}
21. ​ }
 
 
​
 
22.
​ 
 
 
​
23.
​ 
  
 
​ 24. }
​  14  4 ​ 
10
3
3
w
z
n
49c d
h9
4b14
1
3
25. ​ }
 12 ​ 26. }
​  2  ​ 27. 4q r 28. }
​  5  ​
7a
125g
y
4f 3
4
4
29. }
​  5  ​ 30. S 5 }
​ 9 ​ π x 2 31. V 5 }
​ 3 ​ π x 4
9e
32
32. V 5 }
​ 3  ​ π x 6 33. about 1.03 3 1011
34. about 6.1 3 101
Practice Level C
1– 8. Check properties. 1. 25 2. 2187
64
512
3. 1024 4. 256 5. ​ } ​  6. 729 7. }
​ 19,683
  ​ 
27
1
8. ​ }
    
​ 9. 2.139 3 105 10. 9.72 3 1026
125
11. 1.6 3 105 12. 2.0 3 1023 13. 1.0 3 1026
14. 2.5 3 101 15–22. Check properties. 15. x 6
2
π 16m 6n17 26. about 1.665 3 1025 27. a. ​ }3 ​ b. }
​ 6  ​
Algebra 2
Chapter Resource Book
A19