Rewrite the expression with a rational exponent.
51)
49x7y
51)
A)
1
4·
(9x7y)
B)
(9x7y)4
C)
1
(9x7y)4
D)
(9x7y)1/4
Use radical notation to rewrite the expression. Simplify, if possible.
52)
(–64)1/3
52)
A)
–4
B)
4
C)
–4316
D)
–1
4
Rationalize the denominator and simplify.
53)
1
32
53)
A)
32
4
B)
232
C)
32
2
D)
34
2
54)
2x
5x
54)
A)
2 x
B)
2 5x
25x
C)
2 5x
5
D)
10
5
Evaluate.
55)
i23
55)
A)
–i
B)
i
C)
–1
D)
1
Simplify by factoring. Assume that any variable in a radicand represents a positive real number.
56)
596x14
56)
A)
2x 53x4
B)
2x253x
C)
2x25x4
D)
2x253x4
Perform the indicated operation and, if possible, simplify. Assume that all variables represent positive real numbers.
57)
11( 2 – 4 55)
57)
A)
22 + 44 5
B)
22 – 4 605
C)
22 + 4 605
D)
22 – 44 5
Divide and, if possible, simplify.
58)
30xy3
6x
58)
A)
y25y
B)
y230y
C)
y25xy
D)
y 5y
Add or subtract as indicated. You will need to simplify terms to identify like radicals.
59)
38y –3128y
59)
A)
63y
B)
2– 432
C)
432y – 2 3y
D)
23y– 4 32y
Multiply and simplify. Assume that all variables in a radicand represent positive real numbers.
60)
12x·6y
60)
A)
6 2xy
B)
2 6xy
C)
72xy
D)
6xy 2
Solve the formula for the specified variable.
61)
r =2A
for
61)
A)
=2a
R
2
B)
=r2
2A
C)
=2A
r
D)
=2A
r2
Rationalize numerator.
62)
7–2
7+2
62)
A)
51
47 – 14 2
B)
1
C)
47
51 + 14 2
D)
47
51 – 14 2
Solve the equation.
63)
x2– 5x + 9 = x – 2
63)
A)
{5}
B)
{3}
C)
{–5}
D)
–5
2
Multiply and simplify. Assume that all variables represent positive real numbers.
64)
(3 +5)(2+4 5)
64)
A)
26 +6 5
B)
26 +14 5
C)
6+18 5
D)
96
Rewrite the expression with a rational exponent.
65)
10
65)
A)
101/2
B)
102
C)
1
102
D)
1
2·10
Find the cube root.
66)
–
3125
66)
A)
25
B)
5
C)
–5
D)
–125
Rationalize the denominator and simplify.
67)
5
3x
67)
A)
5 3x
3x
B)
14x
C)
5 3x
D)
25 3x
3x
Simplify the expression. Assume that variables can represent any real number.
68)
20x2
68)
A)
2x25
B)
2x 5
C)
2 x 5
D)
5 x 2
Use rational exponents to simplify the expression. If rational exponents appear after simplifying, write the answer in
radical notation.
69)
27 x9
69)
A)
3x
B)
18 x
C)
x
18
D)
x3
Simplify the expression.
70)
72
70)
A)
7
2
B)
7
C)
49
D)
14
Rationalize numerator.
71)
36
35
71)
A)
6
3180
B)
3150
5
C)
6
330
D)
330
5
Rationalize the denominator and simplify.
72)
54
y6
72)
A)
54y4
y2
B)
y254
C)
454y
y2
D)
54y2
Perform the indicated operation and, if possible, simplify. Assume that all variables represent positive real numbers.
73)
48x3y·46xy2
73)
A)
x43y3
B)
6xy
C)
x46y3
D)
2x 43y3
Perform the indicated operation. Write the result in the form a +
bi.
74)
74)
(6 – 4i)(2+ 9i)
A)
48 – 46i
B)
–36i2+ 46i + 12
C)
–24 – 62i
D)
48 + 46i
22
Use radical notation to rewrite the expression. Simplify, if possible.
75)
(–27)4/3
75)
A)
729
B)
not a real number
C)
–81
D)
81
Solve.
76)
76)
Find the area and perimeter of the rectangle. Simplify each expression.
18 – 1 ft
18 + 1 ft
A)
area: 323 sq ft, perimeter: 12 2+ 2 ft
B)
area: 17 sq ft, perimeter: 12 2 ft
C)
area: 17 sq ft, perimeter: 6 ft
D)
area: (19 +6 2) sq ft, perimeter: 12 2 ft
Evaluate.
77)
i50
77)
A)
–1
B)
i
C)
1
D)
–i
Divide and, if possible, simplify.
78)
160x9
10x
78)
A)
4x8
B)
4 x9
C)
4x410
D)
4x4
Find the indicated root, or state that the expression is not a real number.
79)
3–125
79)
A)
–35
B)
not a real number
C)
–5
D)
5
Use the product rule to multiply.
80)
4 x
16 ·416
y
80)
A)
4 x
y
B)
1
2
4 x
y
C)
24 x
y
D)
8 x
y
Find each product. Write the result in the form a +
bi.
81)
81)
(2 – 4i)(7+ 5i)
A)
–6– 38i
B)
34 – 18i
C)
–20i2– 18i + 14
D)
34 + 18i
24
Find the perimeter or area of the figure as indicated. Express your answer in simplified radical form.
82)
82)
Find the area of the rectangle.
2 ft
14 ft
A)
2 7 sq ft
B)
14 sq ft
C)
28 sq ft
D)
4 7 sq ft
Solve the equation.
83)
5x – 4 =4
83)
A)
12
5
B)
C)
{4}
D)
{16}
Use rational exponents to simplify the radical. If rational exponents appear after simplifying, write the answer in
radical notation.
84)
15 (2y)5
84)
A)
10 2y
B)
32y
C)
32y5
D)
8y3
Add or subtract as indicated. You will need to simplify terms to identify like radicals.
85)
7162 – 6 18 + 2 200
85)
A)
65 2
B)
8 2
C)
7 2
D)
–8 2
Rewrite the expression with a positive rational exponent. Simplify, if possible.
86)
4xy–5/6
86)
A)
1
( 4xy )5/6
B)
1
4xy5/6
C)
4x
y5/6
D)
–4x
y5/6
Find the function value indicated for the function. If necessary, round to two decimal places. If the function value is not
a real number and does not exist, state so.
87)
Evaluate z(x) =x –16 for z(1)
87)
A)
not a real number
B)
15
C)
–3
D)
–15
Simplify the expression. Include absolute value bars where necessary.
88)
5
–1024x5
88)
A)
4x
B)
–4x
C)
– – 4 x
D)
–4 x
26
Rationalize numerator.
89)
x+ 3 y
4 x
89)
A)
x –9y
4x + 12 xy
B)
x –3y
4x – 12 xy
C)
x –9y
4x – 12 xy
D)
x +9y
4x + 12 xy
Evaluate.
90)
i33
90)
A)
1
B)
–1
C)
i
D)
–i
Use the quotient rule to simplify. Assume all variables represent positive real numbers.
91)
25
81
91)
A)
9
5
B)
5
9
C)
1
D)
45
Rationalize numerator.
92)
6
7x
92)
A)
6
6x
B)
6
7x
C)
42x
7x
D)
6
42x
Simplify by factoring. Assume that any variable in a radicand represents a positive real number.
93)
3y11
93)
A)
3y33y2
B)
y8
C)
3y 3y2
D)
y33y2
Rationalize numerator.
94)
17
8z
94)
A)
1
297
B)
17
64z17
C)
1
8z 17
D)
17
8z 17
Solve the equation.
95)
3x – 2 +11 + x = – 1
95)
A)
B)
–5
2
C)
{0}
D)
{5}
Write in terms of i.
96)
–81
96)
A)
9i
B)
±9
C)
–i 9
D)
–9i
Simplify by factoring.
97)
180
97)
A)
30
B)
6 5
C)
5 6
D)
13
Perform the indicated operation and, if possible, simplify. Assume that all variables represent positive real numbers.
98)
35x2·36y
98)
A)
330x2y
B)
x330y
C)
53x2y
D)
6x 3y
Find the perimeter or area of the figure as indicated. Express your answer in simplified radical form.
99)
99)
Find the perimeter of the triangle.
32 m 72 m
112 m
A)
(32 +72 +112) m
B)
14 14 m
C)
(48 +4 7) m
D)
(10 2+4 7) m
Solve the problem.
100)
The distance d in miles that can be seen on the surface of the ocean is given by d =1.6h1/2, where
h is the height in feet above the surface. How high would a platform have to be to see a distance
of 19.5 miles? Round to the nearest foot.
100)
A)
608 ft
B)
149 ft
C)
380 ft
D)
122 ft
Multiply and simplify. Assume that all variables in a radicand represent positive real numbers.
101)
5100 ·510,000
101)
A)
510
B)
51,000,000
C)
10 510
D)
10 510,000
Solve the problem.
102)
102)
The average height of a boy in the United States, from birth through 60 months, can be modeled
by y = 2.9 x+ 20.1 where y is the average height, in inches, of boys who are x months of age.
What would be the expected difference in height between a child 49 months of age and a child 16
months of age?
A)
10.7 in.
B)
48.9 in.
C)
20.3 in.
D)
8.7 in.
Divide and, if possible, simplify.
103)
5128x26y28
54xy–2
103)
A)
2x20y25 5x2
B)
2x25y30
C)
2x25y30 54x2y3
D)
2x5y6
Solve the problem.
104)
104)
The number of centimeters, d, that a spring is compressed from its natural, uncompressed
position is given by the formula d =2W
k, where W is the number of joules of work done to
move the spring and k is the spring constant. If a spring has a spring constant of 0.4, find the
amount of work needed to move the spring 4 centimeters.
A)
3.2 joules
B)
0.8 joules
C)
6.4 joules
D)
16 joules
105)
105)
It has been found that the less income people have, the more likely they are to report that their
health is fair or poor. The function f(x) = – 4.4 x+ 38 models the percentage of Americans
reporting fair or poor health, f(x), in terms of annual income, x, in thousands of dollars. Find and
interpret f(22).
A)
f(22) 18.3; 18.3% of Americans earning $22 thousand annually report fair or poor health.
B)
f(22) 17.4; 22% of Americans earning $17.4 thousand annually report fair or poor health.
C)
f(22) $18.3; 22% of Americans earning $18.3 thousand annually report fair or poor health.
D)
f(22) 17.4; 17.4% of Americans earning $22 thousand annually report fair or poor health.