14. ANSWER: 1
7-3 Rational Exponents
Write each expression in radical form, or write
each radical in exponential form.
2. ANSWER: 16. CCSS TOOLS A weir is used to measure water
flow in a channel. (Refer to the photo on page 410)
For a rectangular broad crested weir, the flow Q in
cubic feet per second is related to the weir length L
in feet and height H of the water by
. Find the water height for a weir
that is 3 feet long and has flow of 38.4 cubic feet
per second.
4. ANSWER: ANSWER: 4 ft
Write each expression in radical form, or write
each radical in exponential form.
Simplify.
6. 18. ANSWER: ANSWER: 3
20. 8. ANSWER: ANSWER: 22. 10. ANSWER: ANSWER: 27
24. 12. ANSWER: ANSWER: Simplify.
Solve each equation.
26. 14. ANSWER: 4
ANSWER: 1
16. CCSS TOOLS A weir is used to measure water
flow in a channel. (Refer to the photo on page 410)
For a rectangular broad crested weir, the flow Q in
cubic feet per second is related to the weir length L
in feet and height H of the water by
eSolutions Manual - Powered by Cognero
. Find the water height for a weir
that is 3 feet long and has flow of 38.4 cubic feet
per second.
28. ANSWER: 10
30. Page 1
ANSWER: Solve each equation.
46. 28. ANSWER: 2
ANSWER: 7-3 Rational
Exponents
10
48. 30. ANSWER: ANSWER: 50. 32. ANSWER: ANSWER: 2
52. 34. ANSWER: 2
ANSWER: 2
54. ANSWER: 36. ANSWER: 56. ANSWER: 38. ANSWER: 125
58. ELECTRICITY The radius r in millimeters of a
platinum wire L centimeters long with resistance 0.1
ohm is
40. ANSWER: 8
.
How long is a wire with radius 0.236 millimeter?
ANSWER: 16 cm
42. Write each expression in radical form, or write
each radical in exponential form.
ANSWER: 16,807
60. ANSWER: 44. ANSWER: Solve each equation.
62. ANSWER: 46. ANSWER: 2
64. 48. ANSWER: eSolutions Manual - Powered by Cognero
ANSWER: Page 2
62. 78. ANSWER: 7-3 Rational Exponents
ANSWER: 1
Solve each equation.
64. 80. ANSWER: 66. ANSWER: 3
82. ANSWER: ANSWER: Simplify.
84. 68. ANSWER: 70. ANSWER: 72. ANSWER: 74. ANSWER: 76. ANSWER: 78. ANSWER: 1
Solve each equation.
eSolutions Manual - Powered by Cognero
80. ANSWER: ANSWER: 11
86. RANDOM WALKS Suppose you go on a walk
where you choose the direction of each step at
random. The path of a molecule in a liquid or a gas,
the path of a foraging animal, and a fluctuating
stock price are all modeled as random walks. The
number of possible random walks w of n steps
where you choose one of d directions at each step
is
.
a. How many steps have been taken in a 2-direction
random walk if there are 4096 possible walks? b. How many steps have been taken in a 4-direction
random walk if there are 65,536 possible walks? c. If a walk of 7 steps has 2187 possible walks, how
many directions could be taken at each step? ANSWER: a. 12
b. 8
c. 3
88. MULTIPLE REPRESENTATIONS In this
problem, you will explore the graph of an
exponential function.
a. TABULAR Copy and complete the table below.
b. GRAPHICAL Graph f (x) by plotting the points
and connecting them with a smooth curve.
c. VERBAL Describe the shape of the graph of f
(x). What are its key features? Is it linear?
ANSWER: a. Page 3
ANSWER: a. 12
b. 8
7-3 Rational
Exponents
c. 3
88. MULTIPLE REPRESENTATIONS In this
problem, you will explore the graph of an
exponential function.
a. TABULAR Copy and complete the table below.
intercept, a y-intercept of 1, the domain is all reals,
the range is all positive reals, it is
increasing over the entire domain, as x approaches
infinity f (x) approaches infinity, as x approaches
negative infinity f (x) approaches 0.
90. CCSS ARGUMENTS Determine whether each
statement is always, sometimes, or never true.
Assume that x is a nonnegative real number.
Explain your reasoning.
a.
b. GRAPHICAL Graph f (x) by plotting the points
and connecting them with a smooth curve.
c. VERBAL Describe the shape of the graph of f
(x). What are its key features? Is it linear?
ANSWER: a. b. b.
c.
d.
e.
f.
ANSWER: a. sometimes; true only when x = 1
b. sometimes; true only when x = 1
c. sometimes; true only when x = 1
d. always; by definition of
e. always;
or x
f. sometimes; true only when x = 1
c.The graph of f (x) = 4x is a curve. It has no xintercept, a y-intercept of 1, the domain is all reals,
the range is all positive reals, it is
increasing over the entire domain, as x approaches
infinity f (x) approaches infinity, as x approaches
negative infinity f (x) approaches 0.
90. CCSS ARGUMENTS Determine whether each
statement is always, sometimes, or never true.
Assume that x is a nonnegative real number.
Explain your reasoning.
a.
b.
c.
d.
eSolutions
e. Manual - Powered by Cognero
f.
92. ERROR ANALYSIS Anna and Jamal are solving
. Is either of them correct?
Explain your reasoning.
ANSWER: Anna; Jamal did not write the expressions with
equal bases before applying the Power Property of
Equality.
94. What is the value of
A5
B 11
C 25
D 35
?
ANSWER: D
Page 4
96. SHORT RESPONSE Find the dimensions of the
rectangle if its perimeter is 52 inches.
102. ANSWER: Anna; Jamal did not write the expressions with
equal bases
before applying the Power Property of
7-3 Rational
Exponents
Equality.
94. What is the value of
A5
B 11
C 25
D 35
?
ANSWER: 104. GARDENING Felipe is planting a flower garden
that is shaped like a trapezoid as shown. 3
Use the formula
to find the area
of the garden.
ANSWER: D
ANSWER: 96. SHORT RESPONSE Find the dimensions of the
rectangle if its perimeter is 52 inches.
15a
2
Write each equation in slope-intercept form.
106. ANSWER: y = 6x + 11
108. ANSWER: 17.5 in. by 8.5 in.
ANSWER: Simplify each expression. Assume that no
denominator equals zero. 110. ANSWER: 98. ANSWER: Find each power.
5
112. 10
ANSWER: 100,000
100. ANSWER: 114. ANSWER: 0.0001
102. ANSWER: 104. GARDENING Felipe is planting a flower garden
that is shaped like a trapezoid as shown. 3
Use the formula
to find the area
of the garden.
eSolutions Manual - Powered by Cognero
Page 5