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Math Problems
Precalculus
Operations with rational exponents
Select the answer which is equivalent to the given expression using your calculator.
\newline
tan
(
arccos
8
9
)
\tan \left(\arccos \frac{8}{9}\right)
tan
(
arccos
9
8
)
\newline
17
8
\frac{\sqrt{17}}{8}
8
17
\newline
9
8
\frac{9}{8}
8
9
\newline
17
9
\frac{\sqrt{17}}{9}
9
17
\newline
9
17
\frac{9}{\sqrt{17}}
17
9
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Select the answer which is equivalent to the given expression using your calculator.
\newline
(
5
a
)
3
5
b
2
a
=
−
2
and
b
=
−
3
\begin{array}{c} \frac{(5 a)^{3}}{5 b^{2}} \\ a=-2 \text { and } b=-3 \end{array}
5
b
2
(
5
a
)
3
a
=
−
2
and
b
=
−
3
\newline
5000
9
\frac{5000}{9}
9
5000
\newline
−
5000
9
-\frac{5000}{9}
−
9
5000
\newline
−
200
9
-\frac{200}{9}
−
9
200
\newline
200
9
\frac{200}{9}
9
200
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Select the answer which is equivalent to the given expression using your calculator.
\newline
8
a
4
(
243
b
)
2
5
a
=
6
and
b
=
32
\begin{array}{c} \frac{8 a^{4}}{(243 b)^{\frac{2}{5}}} \\ a=6 \text { and } b=32 \end{array}
(
243
b
)
5
2
8
a
4
a
=
6
and
b
=
32
\newline
288
288
288
\newline
−
288
-288
−
288
\newline
864
864
864
\newline
−
864
-864
−
864
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Select the answer which is equivalent to the given expression using your calculator.
\newline
(
−
5
a
)
2
(
32
b
)
3
5
a
=
−
5
and
b
=
3125
\begin{array}{c} \frac{(-5 a)^{2}}{(32 b)^{\frac{3}{5}}} \\ a=-5 \text { and } b=3125 \end{array}
(
32
b
)
5
3
(
−
5
a
)
2
a
=
−
5
and
b
=
3125
\newline
5
8
\frac{5}{8}
8
5
\newline
5
16
\frac{5}{16}
16
5
\newline
−
5
8
-\frac{5}{8}
−
8
5
\newline
−
5
16
-\frac{5}{16}
−
16
5
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Select the answer which is equivalent to the given expression using your calculator.
\newline
−
10
a
3
2
(
32
b
)
2
5
\frac{-10 a^{\frac{3}{2}}}{(32 b)^{\frac{2}{5}}}
(
32
b
)
5
2
−
10
a
2
3
\newline
a
=
16
and
b
=
243
a=16 \text { and } b=243
a
=
16
and
b
=
243
\newline
160
9
\frac{160}{9}
9
160
\newline
−
160
9
-\frac{160}{9}
−
9
160
\newline
−
160
27
-\frac{160}{27}
−
27
160
\newline
160
27
\frac{160}{27}
27
160
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Select the answer which is equivalent to the given expression using your calculator.
\newline
2
a
−
3
−
8
b
−
4
a
=
−
6
and
b
=
3
\begin{array}{c} \frac{2 a^{-3}}{-8 b^{-4}} \\ a=-6 \text { and } b=3 \end{array}
−
8
b
−
4
2
a
−
3
a
=
−
6
and
b
=
3
\newline
−
3
32
-\frac{3}{32}
−
32
3
\newline
3
32
\frac{3}{32}
32
3
\newline
3
8
\frac{3}{8}
8
3
\newline
−
3
8
-\frac{3}{8}
−
8
3
Get tutor help
Select the answer which is equivalent to the given expression using your calculator.
\newline
−
9
a
4
(
243
b
)
2
5
\frac{-9 a^{4}}{(243 b)^{\frac{2}{5}}}
(
243
b
)
5
2
−
9
a
4
\newline
a
=
−
6
a=-6
a
=
−
6
and
b
=
1024
b=1024
b
=
1024
\newline
−
81
-81
−
81
\newline
81
81
81
\newline
3
3
3
\newline
−
3
-3
−
3
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Find the sum of the first
7
7
7
terms of the following series, to the nearest integer.
\newline
6
,
9
2
,
27
8
,
…
6, \frac{9}{2}, \frac{27}{8}, \ldots
6
,
2
9
,
8
27
,
…
\newline
Answer:
Get tutor help
Find the sum of the first
8
8
8
terms of the following series, to the nearest integer.
\newline
3
,
15
4
,
75
16
,
…
3, \frac{15}{4}, \frac{75}{16}, \ldots
3
,
4
15
,
16
75
,
…
\newline
Answer:
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Express the given expression as an integer or as a fraction in simplest form.
\newline
log
3
(
1
3
5
4
)
\log _{3}\left(\frac{1}{\sqrt[4]{3^{5}}}\right)
lo
g
3
(
4
3
5
1
)
\newline
Answer:
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Express the given expression as an integer or as a fraction in simplest form.
\newline
(
2
log
2
1
3
)
\left(2^{\log _{2} \frac{1}{3}}\right)
(
2
l
o
g
2
3
1
)
\newline
Answer:
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Express the given expression as an integer or as a fraction in simplest form.
\newline
(
9
log
9
18
+
log
9
4
)
\left(9^{\log _{9} 18+\log _{9} 4}\right)
(
9
l
o
g
9
18
+
l
o
g
9
4
)
\newline
Answer:
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Express the given expression as an integer or as a fraction in simplest form.
\newline
(
1
0
log
3
5
)
\left(10^{\log \frac{3}{5}}\right)
(
1
0
l
o
g
5
3
)
\newline
Answer:
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Express the given expression as an integer or as a fraction in simplest form.
\newline
log
8
(
1
8
7
)
\log _{8}\left(\frac{1}{8^{7}}\right)
lo
g
8
(
8
7
1
)
\newline
Answer:
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Find the
14
14
14
th term of the arithmetic sequence
−
2
x
−
3
,
−
6
x
−
9
,
−
10
x
−
15
,
…
-2 x-3,-6 x-9,-10 x-15, \ldots
−
2
x
−
3
,
−
6
x
−
9
,
−
10
x
−
15
,
…
\newline
Answer:
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Find the
12
12
12
th term of the geometric sequence shown below.
\newline
2
x
2
,
4
x
4
,
8
x
6
,
…
2 x^{2}, 4 x^{4}, 8 x^{6}, \ldots
2
x
2
,
4
x
4
,
8
x
6
,
…
\newline
Answer:
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Find the
12
12
12
th term of the geometric sequence shown below.
\newline
4
x
4
,
16
x
7
,
64
x
10
,
…
4 x^{4}, 16 x^{7}, 64 x^{10}, \ldots
4
x
4
,
16
x
7
,
64
x
10
,
…
\newline
Answer:
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Find the
9
9
9
th term of the geometric sequence shown below.
\newline
7
x
3
,
−
14
x
8
,
28
x
13
,
…
7 x^{3},-14 x^{8}, 28 x^{13}, \ldots
7
x
3
,
−
14
x
8
,
28
x
13
,
…
\newline
Answer:
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Find the
12
12
12
th term of the geometric sequence shown below.
\newline
x
3
,
3
x
4
,
9
x
5
,
…
x^{3}, 3 x^{4}, 9 x^{5}, \ldots
x
3
,
3
x
4
,
9
x
5
,
…
\newline
Answer:
Get tutor help
Find the
8
8
8
th term of the geometric sequence shown below.
\newline
−
9
x
6
,
−
9
x
11
,
−
9
x
16
,
…
-9 x^{6},-9 x^{11},-9 x^{16}, \ldots
−
9
x
6
,
−
9
x
11
,
−
9
x
16
,
…
\newline
Answer:
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Find the
11
11
11
th term of the geometric sequence shown below.
\newline
−
6
x
8
,
18
x
10
,
−
54
x
12
,
…
-6 x^{8}, 18 x^{10},-54 x^{12}, \ldots
−
6
x
8
,
18
x
10
,
−
54
x
12
,
…
\newline
Answer:
Get tutor help
Find the
8
8
8
th term of the geometric sequence shown below.
\newline
7
x
4
,
28
x
6
,
112
x
8
,
…
7 x^{4}, 28 x^{6}, 112 x^{8}, \ldots
7
x
4
,
28
x
6
,
112
x
8
,
…
\newline
Answer:
Get tutor help
Find the
10
10
10
th term of the geometric sequence shown below.
\newline
x
4
,
5
x
6
,
25
x
8
,
…
x^{4}, 5 x^{6}, 25 x^{8}, \ldots
x
4
,
5
x
6
,
25
x
8
,
…
\newline
Answer:
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Write in exponential notation:
\newline
6
3
6
2
\frac{6^{3}}{6^{2}}
6
2
6
3
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Write in exponential notation:
\newline
2
4
2
7
\frac{2^{4}}{2^{7}}
2
7
2
4
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Select the equivalent expression.
(
8
−
5
2
−
2
)
−
4
=
?
\left(\frac{8^{-5}}{2^{-2}}\right)^{-4}=\,?
(
2
−
2
8
−
5
)
−
4
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
8
20
2
8
\frac{8^{20}}{2^{8}}
2
8
8
20
\newline
(B)
2
6
8
9
\frac{2^{6}}{8^{9}}
8
9
2
6
\newline
(C)
1
8
⋅
2
2
\frac{1}{8\cdot 2^{2}}
8
⋅
2
2
1
Get tutor help
Solve the equation by factoring:
\newline
2
x
3
−
30
x
2
+
108
x
=
0
2 x^{3}-30 x^{2}+108 x=0
2
x
3
−
30
x
2
+
108
x
=
0
\newline
Answer:
x
=
x=
x
=
Get tutor help
Solve the equation by factoring:
\newline
x
3
−
7
x
2
−
8
x
=
0
x^{3}-7 x^{2}-8 x=0
x
3
−
7
x
2
−
8
x
=
0
\newline
Answer:
x
=
x=
x
=
Get tutor help
Solve the equation by factoring:
\newline
15
x
2
−
50
x
−
x
3
=
0
15 x^{2}-50 x-x^{3}=0
15
x
2
−
50
x
−
x
3
=
0
\newline
Answer:
x
=
x=
x
=
Get tutor help
Solve the equation by factoring:
\newline
51
x
2
−
210
x
−
3
x
3
=
0
51 x^{2}-210 x-3 x^{3}=0
51
x
2
−
210
x
−
3
x
3
=
0
\newline
Answer:
x
=
x=
x
=
Get tutor help
Solve the equation by factoring:
\newline
x
3
−
12
x
2
+
32
x
=
0
x^{3}-12 x^{2}+32 x=0
x
3
−
12
x
2
+
32
x
=
0
\newline
Answer:
x
=
x=
x
=
Get tutor help
Solve the equation by factoring:
\newline
36
x
+
12
x
2
−
3
x
3
=
0
36 x+12 x^{2}-3 x^{3}=0
36
x
+
12
x
2
−
3
x
3
=
0
\newline
Answer:
x
=
x=
x
=
Get tutor help
Simplify the following expression completely.
\newline
x
2
−
17
x
+
72
x
2
−
9
x
+
8
\frac{x^{2}-17 x+72}{x^{2}-9 x+8}
x
2
−
9
x
+
8
x
2
−
17
x
+
72
\newline
Answer:
Get tutor help
Simplify the following expression completely.
\newline
x
2
−
12
x
+
20
x
2
−
14
x
+
40
\frac{x^{2}-12 x+20}{x^{2}-14 x+40}
x
2
−
14
x
+
40
x
2
−
12
x
+
20
\newline
Answer:
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Solve for
x
x
x
.
\newline
−
9
8
x
−
9
x
=
9
8
\frac{-9}{8 x}-\frac{9}{x}=\frac{9}{8}
8
x
−
9
−
x
9
=
8
9
\newline
Answer:
x
=
x=
x
=
Get tutor help
Simplify the expression completely if possible.
\newline
x
2
−
11
x
+
24
x
2
−
9
\frac{x^{2}-11 x+24}{x^{2}-9}
x
2
−
9
x
2
−
11
x
+
24
\newline
Answer:
Get tutor help
Simplify the expression completely if possible.
\newline
21
x
3
−
168
x
2
7
x
2
\frac{21 x^{3}-168 x^{2}}{7 x^{2}}
7
x
2
21
x
3
−
168
x
2
\newline
Answer:
Get tutor help
Simplify the expression completely if possible.
\newline
x
2
−
25
2
x
3
+
10
x
2
\frac{x^{2}-25}{2 x^{3}+10 x^{2}}
2
x
3
+
10
x
2
x
2
−
25
\newline
Answer:
Get tutor help
Simplify the expression completely if possible.
\newline
x
2
−
13
x
+
40
5
x
2
−
40
x
\frac{x^{2}-13 x+40}{5 x^{2}-40 x}
5
x
2
−
40
x
x
2
−
13
x
+
40
\newline
Answer:
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Simplify the following expression completely.
\newline
x
2
+
x
−
90
x
2
+
15
x
+
50
\frac{x^{2}+x-90}{x^{2}+15 x+50}
x
2
+
15
x
+
50
x
2
+
x
−
90
\newline
Answer:
Get tutor help
Simplify the following expression completely.
\newline
x
2
+
9
x
+
18
x
2
+
10
x
+
24
\frac{x^{2}+9 x+18}{x^{2}+10 x+24}
x
2
+
10
x
+
24
x
2
+
9
x
+
18
\newline
Answer:
Get tutor help
Simplify the following expression completely.
\newline
x
2
−
13
x
+
30
x
2
−
12
x
+
27
\frac{x^{2}-13 x+30}{x^{2}-12 x+27}
x
2
−
12
x
+
27
x
2
−
13
x
+
30
\newline
Answer:
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Simplify the following expression completely.
\newline
x
2
−
16
x
+
63
x
2
−
19
x
+
90
\frac{x^{2}-16 x+63}{x^{2}-19 x+90}
x
2
−
19
x
+
90
x
2
−
16
x
+
63
\newline
Answer:
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Simplify the following expression completely.
\newline
x
2
−
6
x
−
7
x
2
−
16
x
+
63
\frac{x^{2}-6 x-7}{x^{2}-16 x+63}
x
2
−
16
x
+
63
x
2
−
6
x
−
7
\newline
Answer:
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Simplify the expression completely if possible.
\newline
x
2
−
11
x
+
28
x
2
−
14
x
+
49
\frac{x^{2}-11 x+28}{x^{2}-14 x+49}
x
2
−
14
x
+
49
x
2
−
11
x
+
28
\newline
Answer:
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Simplify the expression completely if possible.
\newline
x
2
−
81
2
x
4
−
10
x
3
\frac{x^{2}-81}{2 x^{4}-10 x^{3}}
2
x
4
−
10
x
3
x
2
−
81
\newline
Answer:
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Simplify the expression completely if possible.
\newline
x
2
−
81
x
3
+
9
x
2
\frac{x^{2}-81}{x^{3}+9 x^{2}}
x
3
+
9
x
2
x
2
−
81
\newline
Answer:
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Solve the equation
2
x
2
+
15
x
+
35
=
x
2
2 x^{2}+15 x+35=x^{2}
2
x
2
+
15
x
+
35
=
x
2
to the nearest tenth.
\newline
Answer:
x
=
x=
x
=
Get tutor help
Evaluate the left hand side to find the value of
a
a
a
in the equation in simplest form.
\newline
x
5
2
x
3
4
=
x
a
\frac{x^{\frac{5}{2}}}{x^{\frac{3}{4}}}=x^{a}
x
4
3
x
2
5
=
x
a
\newline
Answer:
Get tutor help
Evaluate the left hand side to find the value of
a
a
a
in the equation in simplest form.
\newline
x
5
2
x
2
=
x
a
\frac{x^{\frac{5}{2}}}{x^{2}}=x^{a}
x
2
x
2
5
=
x
a
\newline
Answer:
Get tutor help
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