45. 46. 47. 48.
49. 50. 51. 52.
Evaluate each expression. See Examples 4 and 7.
57. 58. 59. 60.
In Exercises 61 and 62, match the expression in Column I with its equivalent expression in
Column II. Choices may be used once, more than once, or not at all.* See Example 7.
III I II- (a) A.
(b) B. 3(c) C.(d) -a- D.- 31
3
b- 1
-
1
3
- a
1
3
b- 1
a-1
3
b- 1
1
3
a1
3
b- 1
a5
4
b- 2
a
4
5
b- 2
a
3
2
b- 3
a
2
3
b- 3
3 -^3
2 -^2
2 -^2
3 -^3
1
3 -^3
1
4 -^2
5 -^1 + 6 -^12 -^1 + 8 -^18 -^1 - 3 -^16 -^1 - 4 -^1
- a-^3 - b-^41 - a 2 -^41 - b 2 -^6
SECTION 5.1 Integer Exponents and Scientific Notation 275
*The authors thank Mitchel Levy of Broward College for his suggestions for these exercises.
- (a) A.
(b) B.(c) C.(d) D.-4
25
- a-
2
5
b- 2
4
25
- a
2
5
b- 2
-
25
4
a-2
5
b- 2
25
4
a2
5
b- 2
Write each result with only positive exponents. Assume that all variables represent nonzero
real numbers. See Example 5.
67. 68. 69. 70.
71. 72. 73. 74.
75. 76. 77. 78.
Simplify each expression. Assume that all variables represent nonzero real numbers. See
Example 6.
87. 88. 89. 90.
Simplify each expression so that no negative exponents appear in the final result. Assume that
all variables represent nonzero real numbers. See Examples 1– 8.
94.k-^5 k-^3 k^4 95. 1 k^22 -^3 k^4 96. 1 x^32 -^4 x^5
35 # 3 -^644 # 4 -^6 a-^3 a^2 a-^4
a- 2 a^4
b^5
b6
a- s^3
t^5
b4
a- 5 n^4
r^2
b3
a- 4 m^2
t
b314 t 23 15 t 24 1 - 6 x^2231 - 2 x^525a4
3
b2
a3
5
b3
1 x^3261 y^524y^5
t^3x^3
y^2s-^4
s-^8r-^3
r-^68
8 -^1
7
7 -^1
5 -^4
52
6 -^3
67
75
7 -^3
64
6 -^2
y^8
y^12r^7
r^10y^14
y^10x^12
x^8