College Algebra 9th txtbk

20 CHAPTER R BASIC ALGEBRAIC OPERATIONS
In Problems 15–20, write the numbers in scientific notation.
15. 58,620,000 16. 4,390
17. 0.027 18. 0.11
19. 0.000 000 064 20. 0.000 0325
In Problems 21–26, write each number in standard decimal form.
21. 4 10 3 22. 5 10 6
23. 2.99 10 5 24. 7.75 10 11
25. 3.1 10 7 26. 8.167 10 4
In Problems 27–32, change to radical form. Do not simplify.
32 1 5
27. 28. 29.
30. 32y 2 5
31. x 13 y 1 3
32. (x y) 1 3
In Problems 33–38, change to rational exponent form. Do not
simplify.
33. 1361 34. 2 3 17 2 35. 4x2 5 y 3
36. 2 4 7x 3 y 2 37. 2 3 x 2 y 2 38. 2 3 x 2 2 3 y 2
In Problems 39–50, evaluate each expression that represents a
real number.
100 1 2
39. 40.
41. 1121
42. 1361
125 1 3
43. 44.
45. 1 3 27
46. 1 3 64
47. 1 4 16
48. 1 6 1
9 3 2
49. 50.
In Problems 51–64, simplify and express answers using positive
exponents only.
51. x 5 x 2
52. y 6 y 8 53. (2y)(3y 2 )(5y 4 )
54. (6x 3 )(4x 7 )(x 5 ) 55. (a 2 b 3 ) 5 56. (2c 4 d 2 ) 3
57. u 13 u 5 3
58. v 15 v 6 5
59. (x 3 ) 1 6
60. 61. a m2 n 3 2
(49a 4 b 2 ) 1 2
62.
m 4 n 1b
a w4 12
9x 2b
63. 64.
625 3 4
169 1 2
27 2 3
64 4 3
a 8a4 b 3
27a 2 b 3b 13
In Problems 65–86, write in simplified radical form.
65. 1128
66. 1125
67. 127 513
68. 218 118
69. 2 3 5 2 3 25 2 3 625 70. 220 2 3 40 2 3 5
71. 2 3 252 3 10
72. 16114
73. 216m 4 y 8 74. 2 4 16m 4 n 8
4x 1 2
a 6mn2
3m 1 n 2b 3
1
1
3
75. 76. 77.
215
1 3 7
2 3 54
12y 2
4
12
78. 79. 80.
16y
16 2
16 2
12m15
81. x2 5 3 6 x 7 y 11 82. 2a2 3 8a 8 b 13 83.
120m
31y
215 312 312 213
84. 85. 86.
21y 3 515 212 313 212
87. What is the result of entering 2 32 on a calculator?
88. Refer to Problem 87. What is the difference between and
(2 3 ) 2 ? Which agrees with the value of 2 32
obtained with a calculator?
APPLICATIONS
89. ECONOMICS If in the United States in 2007 the national debt
was about $8,868,000,000,000 and the population was about
301,000,000, estimate to three significant digits each individual’s
share of the national debt. Write your answer in scientific notation
and in standard decimal form.
90. ECONOMICS If in the United States in 2007 the gross domestic
product (GDP) was about $14,074,000,000,000 and the population
was about 301,000,000, estimate to three significant digits the GDP
per person. Write your answer in scientific notation and in standard
decimal form.
91. ECONOMICS The number of units N of a finished product produced
from the use of x units of labor and y units of capital for a
particular Third World country is approximated by
N 10x 3 4 y 1 4
Estimate how many units of a finished product will be produced using
256 units of labor and 81 units of capital.
92. ECONOMICS The number of units N of a finished product produced
by a particular automobile company where x units of labor
and y units of capital are used is approximated by
N 50x 1 2 y 1 2
Estimate how many units will be produced using 256 units of labor
and 144 units of capital.
93. BRAKING DISTANCE R. A. Moyer of Iowa State College found,
in comprehensive tests carried out on 41 wet pavements, that the
braking distance d (in feet) for a particular automobile traveling at
v miles per hour was given approximately by
d 0.0212v 7 3
2 (32 )
Approximate the braking distance to the nearest foot for the car
traveling on wet pavement at 70 miles per hour.
94. BRAKING DISTANCE Approximately how many feet would it
take the car in Problem 93 to stop on wet pavement if it were traveling
at 50 miles per hour? (Compute answer to the nearest foot.)