Use properties of rational exponents to simplify the expression. Assume that any variables represent positive numbers.
74)
x5/2 x–2/3
x–1/7
74)
A)
x83/42
B)
1
x83/42
C)
x71/42
D)
1
x71/42
Divide and simplify to the form a +
bi.
75)
5+ 3i
5– 4i
75)
A)
37
41 +5
41 i
B)
13
9+35
9i
C)
13
41 +35
41 i
D)
37
9+35
9i
Simplify by factoring. Assume that any variable in a radicand represents a positive real number.
76)
5(x + k)14
76)
A)
x2+ 9 5(x + k)4
B)
(x + k)25(x + k)4
C)
(x + k)25x + k
D)
(x + k) 5 x + k
Use the quotient rule to simplify. Assume all variables represent positive real numbers.
77)
48x2y
49
77)
A)
4x 3y
7
B)
4 3x2y
7
C)
16x 3y
D)
x 48y
7
21
Rationalize the denominator.
78)
10 –3
10 +3
78)
A)
97 – 20 3
103
B)
1
C)
103 + 20 3
97
D)
103 – 20 3
97
Rewrite the expression with a rational exponent.
79)
5y 9x8
79)
A)
5yx8
9
B)
5yx8/9
C)
5yx9/8
D)
(5yx)8/9
B
Add or subtract as indicated.
80)
7 7 – 5 7
80)
A)
2 7
B)
–35 14
C)
12 7
D)
214
A
Find each product. Write the result in the form a +
bi.
81)
(2 + 4i)(7+ 4i)
81)
A)
30 + 20i
B)
–2+ 36i
C)
–2– 36i
D)
16i2+ 36i + 14
B
22
D
Simplify the expression. Assume that variables can represent any real number.
82)
3–27
k15
82)
A)
–3
k15
B)
–3
k5
C)
3
k5
D)
27
k5
Add or subtract as indicated. You will need to simplify terms to identify like radicals.
83)
–6 2 – 5 18
83)
A)
–21 2
B)
21 2
C)
–11 2
D)
–9 2
A
Find the indicated function value for the function.
84)
Evaluate f(x) =3x +6 for f(–70)
84)
A)
–64
B)
–4
C)
not a real number
D)
4
B
Solve.
85)
Find the area and perimeter of the rectangle. Simplify each expression.
27 – 1 ft
27 + 1 ft
85)
A)
area: 26 sq ft, perimeter: 12 3 ft
B)
area: 26 sq ft, perimeter: 6 ft
C)
area: 728 sq ft, perimeter: 12 3+ 2 ft
D)
area: (28 +6 3) sq ft, perimeter: 12 3 ft
A
B
Express the function, f, in simplified form. Assume that x can be any real number.
86)
f(x) =
316(x – 3)7
86)
A)
f(x) =2(x – 3)32(x – 3)
B)
f(x) =2(x – 3)23x – 3
C)
f(x) =2(x – 3)232(x – 3)
D)
f(x) =2(x – 3)32(x – 3)
x
Simplify the expression. Include absolute value bars where necessary.
87)
8(x – 3)8
87)
A)
±x – 3
B)
x – 3
C)
x– 3
D)
x – 3
Rationalize numerator.
88)
5
6
88)
A)
6
6
B)
30
6
C)
5
30
D)
5
6
Use rational exponents to simplify the expression. If rational exponents appear after simplifying, write the answer in
radical notation.
89)
27 x9
89)
A)
3x
B)
x
18
C)
18 x
D)
x3
Find the indicated function value for the function.
90)
Evaluate f(x) =3x –27 for f(0)
90)
A)
–3
B)
0
C)
not a real number
D)
3
Solve the problem.
91)
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(
21).
91)
A)
f(21) 17.8; 21% of Americans earning $17.8 thousand annually report fair or poor health.
B)
f(21) 17.8; 17.8% of Americans earning $21 thousand annually report fair or poor health.
C)
f(21) 18.8; 18.8% of Americans earning $21 thousand annually report fair or poor health.
D)
f(21) $18.8; 21% of Americans earning $18.8 thousand annually report fair or poor health.
B
Rationalize numerator.
92)
7+ 4
5
92)
A)
–9
35 + 4 5
B)
11
35 – 4 5
C)
28
335 + 7 5
D)
–9
35 – 4 5
D
Solve the equation.
93)
2x + 3 –x + 1 = 1
93)
A)
{3}
B)
C)
{–3, –1}
D)
{3, –1}
D
25
A
Rewrite the expression with a rational exponent.
94)
415
94)
A)
151/4
B)
154
C)
1
4·15
D)
1
154
Perform the indicated operation. Write the result in the form a +
bi.
95)
(4 – 7i) + (3+ 3i)
95)
A)
–7+ 4i
B)
7– 4i
C)
1+ 10i
D)
7+ 4i
B
Rationalize the denominator. Simplify, if possible. Assume that any variables represent positive real numbers.
96)
39
x
96)
A)
39
x
B)
39
x
C)
39 x
x
D)
39x
x
D
Find each product. Write the result in the form a +
bi.
97)
(4 + 4i)(5– 2i)
97)
A)
28 – 12i
B)
28 + 12i
C)
12 + 28i
D)
–8i2+ 12i + 20
B
Evaluate.
98)
i16 +i14
98)
A)
2
B)
2i
C)
–2
D)
0
D
26
A
Divide and, if possible, simplify.
99)
96a3b3
4a–1b–2
99)
A)
2a2b26
B)
a2b2384b
4
C)
2a 6b
D)
2a2b26b
Use radical notation to rewrite the expression. Simplify, if possible.
100)
–161/4
100)
A)
–42
B)
2
C)
–1
2
D)
–2
Solve the equation.
101)
2x2– 6 = x
101)
A)
{ 6, –6}
B)
C)
{ 6}
D)
{6, –6}
Use radical notation to rewrite the expression. Simplify, if possible.
102)
(xy)1/4
102)
A)
4xy
4
B)
x4y4
C)
1
4xy
D)
4xy
27
Multiply and simplify. Assume that all variables in a radicand represent positive real numbers.
103)
320x10y·
325x13y16
103)
A)
5x6y5325x2y2
B)
5x7y53x2y2
C)
5x7y534x2y
D)
5x7y534x2y2
Write in terms of i.
104)
–289
104)
A)
–i17
B)
–17i
C)
17i
D)
±17
C
Perform the indicated operation. Write the result in the form a +
bi.
105)
(8 + 9i) – (–9+ i)
105)
A)
–17 – 8i
B)
–1+ 10i
C)
17 – 8i
D)
17 + 8i
D
Use rational exponents to simplify the radical. If rational exponents appear after simplifying, write the answer in radical
notation.
106)
5y4
10 y3
106)
A)
10 y
B)
y2
C)
y5
D)
2y
D
Evaluate.
107)
i38
107)
A)
i
B)
–i
C)
–1
D)
1
C
D
Rationalize the denominator.
108)
5+2
5–2
108)
A)
7+ 2 10
3
B)
7+ 2 10
21
C)
29 + 2 10
3
D)
29 + 2 10
21
Rationalize the denominator and simplify.
109)
1
11x
109)
A)
11x
11x
B)
11x
121x2
C)
11x
D)
1
Rationalize the denominator.
110)
5
13 + 3
110)
A)
65 + 3 5
4
B)
65 – 3 5
4
C)
65 – 3 5
16
D)
365 + 13 39
5
Rationalize the denominator and simplify.
111)
5x
3x
111)
A)
5 x
B)
5 3x
9x
C)
15
3
D)
5 3x
3
Evaluate.
112)
i57
112)
A)
–i
B)
i
C)
1
D)
–1
Solve the equation.
113)
x + 6 +2 – x = 4
113)
A)
{0}
B)
{–2}
C)
{31, –2}
D)
{2, –2}
Divide and, if possible, simplify.
114)
480x9y17
45xy–2
114)
A)
2xy 4y3
B)
2x2y44y3
C)
2x8y19 4xy2
D)
x2y44xy3
Rewrite the expression with a rational exponent.
115)
6
xy2
115)
A)
1
(xy2)6
B)
(xy2)6
C)
(xy2)1/6
D)
x1/6y2
Perform the indicated operation and, if possible, simplify. Assume that all variables represent positive real numbers.
116)
9 2 + 3 50
116)
A)
–24 2
B)
24 2
C)
12 2
D)
6 2
30
Use the quotient rule to simplify. Assume all variables represent positive real numbers.
117)
10
x4
117)
A)
10x4
x4
B)
10
x4
C)
10
x2
D)
10
x
Use rational exponents to simplify the radical. If rational exponents appear after simplifying, write the answer in radical
notation.
118)
x·7x
118)
A)
14 x9
B)
9x
C)
14 x
D)
x9x
Solve the equation.
119)
x + 1 =6
119)
A)
{49}
B)
{35}
C)
{36}
D)
{37}
Use the product rule to multiply.
120)
x +6·x –6
120)
A)
2x
B)
x2–36
C)
x2+12x +36
D)
x2–36
31
Solve the equation.
121)
9x – 8 =8
121)
A)
B)
{8}
C)
{64}
D)
56
9
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.
122)
Evaluate t(x) =x –4 for t(104)
122)
A)
not a real number
B)
8.2
C)
10.2t
D)
10
Evaluate.
123)
i55
123)
A)
–1
B)
i
C)
–i
D)
1
Use radical notation to rewrite the expression. Simplify, if possible.
124)
(xy)2/7
124)
A)
7xy2
B)
(xy)2
7
C)
7(xy)2
D)
2(xy)7
Simplify by factoring.
125)
3
–27a11b10
125)
A)
3ab 3a4b4
B)
3 a10b11
C)
3a2b 3a3b3
D)
–3a3b33a2b
Find the x–intercept(s) of the graph of the function without graphing the function.
126)
f(x) =x +5–x–1
126)
A)
16
B)
4
C)
no x–intercepts
D)
2
Multiply and simplify. Assume that all variables represent positive real numbers.
127)
(12 +z)( 12 –z)
127)
A)
12 – z
B)
12 – 2 12z
C)
12 – 2 z
D)
12z
Simplify by factoring. Assume that any variable in a radicand represents a positive real number.
128)
9y29
128)
A)
y20 9y9
B)
y99y2
C)
y39y2
D)
y20
Rewrite the expression with a positive rational exponent. Simplify, if possible.
129)
4xy–3/6
129)
A)
1
( 4xy )3/6
B)
1
4xy3/6
C)
–4x
y3/6
D)
4x
y3/6
Solve.
130)
The radius required for a cone to have a volume V and a height h is given by the equation r =
3V
h
1/2.
Find the necessary radius to have a cone with the V =314 cubic inches and h =3 inches. Use
3.14 and round to the nearest whole number.
130)
A)
45 in.
B)
15 in.
C)
10 in.
D)
50 in.
Find the square root if it is a real number, or state that the expression is not a real number.
131)
–361
131)
A)
–180
B)
not a real number
C)
19
D)
–19
Find each product. Write the result in the form a +
bi.
132)
–64 · – 100
132)
A)
80i2
B)
–80i
C)
80
D)
–80
Use radical notation to rewrite the expression. Simplify, if possible.
133)
2164/3
133)
A)
1296
B)
46,656
C)
279,936
D)
7776
Provide an appropriate response.
134)
Simplify: (x–2/5y3/4)1/3
134)
A)
–x2/15y1/4
B)
y1/4
x2/15
C)
x2/15y1/4
D)
x–1/15y26/3
Perform the indicated operation. Write the result in the form a +
bi.
135)
(–4+ 8i) – 7
135)
A)
–11 + 8i
B)
3– 8i
C)
11 – 8i
D)
3+ 8i
A
Solve the problem.
136)
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 0.2, find the amount of work
needed to move the spring 7 centimeters.
136)
A)
0.7 joules
B)
9.8 joules
C)
4.9 joules
D)
49 joules
C
Perform the indicated operation. Write the result in the form a +
bi.
137)
(3 + 3i) – (–8+ i)
137)
A)
11 + 2i
B)
–5+ 4i
C)
11 – 2i
D)
–11 – 2i
A
Add or subtract as indicated.
138)
833+ 10 33
138)
A)
233
B)
18 33
C)
18 36
D)
18 39
B
35
B
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.
139)
Evaluate c(x) =x +12 for c(–3)
139)
A)
3
B)
1.73
C)
not a real number
D)
–3
Find the indicated root, or state that the expression is not a real number.
140)
4–16
140)
A)
–4
B)
2
C)
not a real number
D)
–2
C
Simplify the expression. Include absolute value bars where necessary.
141)
3(–5)3
141)
A)
(–5)3
B)
–5
C)
5
D)
–5
B
Find the square root if it is a real number, or state that the expression is not a real number.
142)
49
142)
A)
1
49
B)
2401
C)
not a real number
D)
7
D
36
A
Simplify the expression.
143)
–49x8
143)
A)
7x4
B)
–7x4
C)
–7x8
D)
–49x4
Solve the problem.
144)
When an object is dropped to the ground from a height of h meters, the time it takes for the object
to reach the ground is given by the equation t =h
4.9 , where t is measured in seconds. If an object
hits the ground after falling for 3 seconds, find the height from which the object was dropped.
144)
A)
147 m
B)
441 m
C)
44.1 m
D)
14.7 m
C
Write in terms of i.
145)
3– – 50
145)
A)
3–5i –2
B)
3–5 2i
C)
3–5i 2
D)
3+5i 2
C
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.
146)
Evaluate f(x) = – 2x +7 for f(9)
146)
A)
–2.24
B)
–5
C)
not a real number
D)
5
B
Multiply and simplify. Assume that all variables in a radicand represent positive real numbers.
147)
30x·5x
147)
A)
5 6x
B)
5x26
C)
x150
D)
5x 6
D
B
Simplify by factoring. Assume that any variable in a radicand represents a positive real number.
148)
310,000x8y6
148)
A)
10x2y2310x2
B)
x2y2310x2
C)
10x2y23x2
D)
10xy 310x2
Rewrite the expression with a rational exponent.
149)
54x12y
149)
A)
(4x12y)5
B)
1
(4x12y)5
C)
1
5· (4x12y)
D)
(4x12y)1/5
150)
x3
150)
A)
x3
2
B)
x2
3
C)
x3/2
D)
x2/3
Add or subtract as indicated. You will need to simplify terms to identify like radicals.
151)
3256x4–332x
151)
A)
(4x –2) 34x
B)
(4x –3) 3x
C)
x3224x
D)
(x –2) 34x
Write in terms of i.
152)
–153
152)
A)
–3i 17
B)
317
C)
–317
D)
3i 17
Find the cube root.
153)
–
327
153)
A)
3
B)
9
C)
–27
D)
–3
Express the function, f, in simplified form. Assume that x can be any real number.
154)
f(x) =3x2– 24x + 48
154)
A)
f(x) = (x + 4) 3
B)
f(x) =(x + 4) 3
x
C)
f(x) = x 51 – 24x
D)
f(x) =x – 4 3
Write in terms of i.
155)
–1600
155)
A)
–40i
B)
i40
C)
±40
D)
40i
Use the product rule to multiply.
156)
8( x – 4 )6·8 x – 4
156)
A)
8( x – 4)7
B)
7( x – 4)6
C)
8
( x2– 16)6
D)
8( 2x – 8)6
Perform the indicated operation. Write the result in the form a +
bi.
157)
Simplify: i47
157)
A)
1
B)
i
C)
–1
D)
–i
Add or subtract as indicated.
158)
16 13 + 2 13
158)
A)
–13 13
B)
–19 13
C)
18 13
D)
14 13
Add or subtract as indicated. You will need to simplify terms to identify like radicals.
159)
7108 + 3 75
159)
A)
57 3
B)
–27 3
C)
–57 3
D)
27 3
Rationalize numerator.
160)
7–10
7+10
160)
A)
59
39 – 14 10
B)
39
59 + 14 10
C)
39
59 – 14 10
D)
1
Perform the indicated operation and, if possible, simplify. Assume that all variables represent positive real numbers.
161)
48x3y·412xy2
161)
A)
2x 46y3
B)
x46y3
C)
12xy
D)
x412y3
Multiply and simplify. Assume that all variables in a radicand represent positive real numbers.
162)
18xy ·6xy2
162)
A)
xy 108y
B)
6x2y23y
C)
6xy 3y
D)
6xy23