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Math Problems
Precalculus
Operations with rational exponents
Evaluate the left hand side to find the value of
a
a
a
in the equation in simplest form.
\newline
(
x
5
6
)
1
4
=
x
a
\left(x^{\frac{5}{6}}\right)^{\frac{1}{4}}=x^{a}
(
x
6
5
)
4
1
=
x
a
\newline
Answer:
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Evaluate the left hand side to find the value of
a
a
a
in the equation in simplest form.
\newline
(
x
2
)
6
5
=
x
a
\left(x^{2}\right)^{\frac{6}{5}}=x^{a}
(
x
2
)
5
6
=
x
a
\newline
Answer:
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Evaluate the left hand side to find the value of
a
a
a
in the equation in simplest form.
\newline
x
2
3
x
4
5
=
x
a
x^{\frac{2}{3}} x^{\frac{4}{5}}=x^{a}
x
3
2
x
5
4
=
x
a
\newline
Answer:
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Evaluate the left hand side to find the value of
a
a
a
in the equation in simplest form.
\newline
x
3
2
x
5
6
=
x
a
\frac{x^{\frac{3}{2}}}{x^{\frac{5}{6}}}=x^{a}
x
6
5
x
2
3
=
x
a
\newline
Answer:
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Evaluate the left hand side to find the value of
a
a
a
in the equation in simplest form.
\newline
x
2
x
1
5
=
x
a
\frac{x^{2}}{x^{\frac{1}{5}}}=x^{a}
x
5
1
x
2
=
x
a
\newline
Answer:
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Evaluate the left hand side to find the value of
a
a
a
in the equation in simplest form.
\newline
x
3
x
1
4
=
x
a
\frac{x^{3}}{x^{\frac{1}{4}}}=x^{a}
x
4
1
x
3
=
x
a
\newline
Answer:
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Evaluate the left hand side to find the value of
a
a
a
in the equation in simplest form.
\newline
(
x
4
5
)
5
3
=
x
a
\left(x^{\frac{4}{5}}\right)^{\frac{5}{3}}=x^{a}
(
x
5
4
)
3
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
2
)
1
3
=
x
a
\left(x^{2}\right)^{\frac{1}{3}}=x^{a}
(
x
2
)
3
1
=
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
2
x
6
5
=
x
a
\frac{x^{2}}{x^{\frac{6}{5}}}=x^{a}
x
5
6
x
2
=
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
3
2
)
5
6
=
x
a
\left(x^{\frac{3}{2}}\right)^{\frac{5}{6}}=x^{a}
(
x
2
3
)
6
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
3
x
1
6
=
x
a
x^{\frac{5}{3}} x^{\frac{1}{6}}=x^{a}
x
3
5
x
6
1
=
x
a
\newline
Answer:
Get tutor help
Fully simplify.
\newline
−
7
y
5
(
−
13
x
2
y
)
-7 y^{5}\left(-13 x^{2} y\right)
−
7
y
5
(
−
13
x
2
y
)
\newline
Answer:
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Fully simplify.
\newline
−
6
x
4
y
3
(
14
x
2
y
5
)
-6 x^{4} y^{3}\left(14 x^{2} y^{5}\right)
−
6
x
4
y
3
(
14
x
2
y
5
)
\newline
Answer:
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Fully simplify.
\newline
13
y
3
(
−
5
x
2
y
4
)
13 y^{3}\left(-5 x^{2} y^{4}\right)
13
y
3
(
−
5
x
2
y
4
)
\newline
Answer:
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The expression
1
0
5
6
⋅
1
0
2
3
\sqrt[6]{10^{5}} \cdot \sqrt[3]{10^{2}}
6
1
0
5
⋅
3
1
0
2
is equivalent to
\newline
1
0
5
9
10^{\frac{5}{9}}
1
0
9
5
\newline
10
0
5
9
100^{\frac{5}{9}}
10
0
9
5
\newline
1
0
3
2
10^{\frac{3}{2}}
1
0
2
3
\newline
10
0
3
2
100^{\frac{3}{2}}
10
0
2
3
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The expression
1
0
4
3
⋅
10
3
\sqrt[3]{10^{4}} \cdot \sqrt[3]{10}
3
1
0
4
⋅
3
10
is equivalent to
\newline
1
0
4
9
10^{\frac{4}{9}}
1
0
9
4
\newline
10
0
5
3
100^{\frac{5}{3}}
10
0
3
5
\newline
1
0
5
3
10^{\frac{5}{3}}
1
0
3
5
\newline
10
0
4
9
100^{\frac{4}{9}}
10
0
9
4
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Given
x
>
0
x>0
x
>
0
and
y
>
0
y>0
y
>
0
, select the expression that is equivalent to
\newline
216
x
12
y
8
3
\sqrt[3]{216 x^{12} y^{8}}
3
216
x
12
y
8
\newline
72
x
4
y
8
3
72 x^{4} y^{\frac{8}{3}}
72
x
4
y
3
8
\newline
72
x
1
4
y
3
8
72 x^{\frac{1}{4}} y^{\frac{3}{8}}
72
x
4
1
y
8
3
\newline
6
x
1
4
y
3
8
6 x^{\frac{1}{4}} y^{\frac{3}{8}}
6
x
4
1
y
8
3
\newline
6
x
4
y
8
3
6 x^{4} y^{\frac{8}{3}}
6
x
4
y
3
8
Get tutor help
Given
x
>
0
x>0
x
>
0
and
y
>
0
y>0
y
>
0
, select the expression that is equivalent to
\newline
−
36
x
4
y
10
\sqrt{-36 x^{4} y^{10}}
−
36
x
4
y
10
\newline
−
6
x
1
2
y
1
5
-6 x^{\frac{1}{2}} y^{\frac{1}{5}}
−
6
x
2
1
y
5
1
\newline
6
i
x
2
y
5
6 i x^{2} y^{5}
6
i
x
2
y
5
\newline
−
6
x
2
y
5
-6 x^{2} y^{5}
−
6
x
2
y
5
\newline
6
i
x
1
2
y
1
5
6 i x^{\frac{1}{2}} y^{\frac{1}{5}}
6
i
x
2
1
y
5
1
Get tutor help
Given
x
>
0
x>0
x
>
0
and
y
>
0
y>0
y
>
0
, select the expression that is equivalent to
\newline
256
x
18
y
16
4
\sqrt[4]{256 x^{18} y^{16}}
4
256
x
18
y
16
\newline
4
x
9
2
y
4
4 x^{\frac{9}{2}} y^{4}
4
x
2
9
y
4
\newline
4
x
2
9
y
1
4
4 x^{\frac{2}{9}} y^{\frac{1}{4}}
4
x
9
2
y
4
1
\newline
64
x
2
9
y
1
4
64 x^{\frac{2}{9}} y^{\frac{1}{4}}
64
x
9
2
y
4
1
\newline
64
x
9
2
y
4
64 x^{\frac{9}{2}} y^{4}
64
x
2
9
y
4
Get tutor help
Given
x
>
0
x>0
x
>
0
and
y
>
0
y>0
y
>
0
, select the expression that is equivalent to
\newline
64
x
8
y
5
\sqrt{64 x^{8} y^{5}}
64
x
8
y
5
\newline
32
x
4
y
5
2
32 x^{4} y^{\frac{5}{2}}
32
x
4
y
2
5
\newline
32
x
1
4
y
2
5
32 x^{\frac{1}{4}} y^{\frac{2}{5}}
32
x
4
1
y
5
2
\newline
8
x
1
4
y
2
5
8 x^{\frac{1}{4}} \boldsymbol{y}^{\frac{2}{5}}
8
x
4
1
y
5
2
\newline
8
x
4
y
5
2
8 x^{4} y^{\frac{5}{2}}
8
x
4
y
2
5
Get tutor help
Given
x
>
0
x>0
x
>
0
and
y
>
0
y>0
y
>
0
, select the expression that is equivalent to
\newline
256
x
8
y
14
4
\sqrt[4]{256 x^{8} y^{14}}
4
256
x
8
y
14
\newline
4
x
32
y
56
4 x^{32} y^{56}
4
x
32
y
56
\newline
64
x
2
y
7
2
64 x^{2} y^{\frac{7}{2}}
64
x
2
y
2
7
\newline
64
x
32
y
56
64 x^{32} y^{56}
64
x
32
y
56
\newline
4
x
2
y
7
2
4 x^{2} y^{\frac{7}{2}}
4
x
2
y
2
7
Get tutor help
Given
x
>
0
x>0
x
>
0
and
y
>
0
y>0
y
>
0
, select the expression that is equivalent to
\newline
216
x
10
y
6
3
\sqrt[3]{216 x^{10} y^{6}}
3
216
x
10
y
6
\newline
6
x
10
3
y
2
6 x^{\frac{10}{3}} y^{2}
6
x
3
10
y
2
\newline
72
x
10
3
y
2
72 x^{\frac{10}{3}} y^{2}
72
x
3
10
y
2
\newline
72
x
30
y
18
72 x^{30} y^{18}
72
x
30
y
18
\newline
6
x
30
y
18
6 x^{30} y^{18}
6
x
30
y
18
Get tutor help
Given
x
>
0
x>0
x
>
0
and
y
>
0
y>0
y
>
0
, select the expression that is equivalent to
\newline
81
x
18
y
8
4
\sqrt[4]{81 x^{18} y^{8}}
4
81
x
18
y
8
\newline
9
x
2
9
y
1
2
9 x^{\frac{2}{9}} y^{\frac{1}{2}}
9
x
9
2
y
2
1
\newline
9
x
9
2
y
2
9 x^{\frac{9}{2}} y^{2}
9
x
2
9
y
2
\newline
3
x
2
9
y
1
2
3 x^{\frac{2}{9}} y^{\frac{1}{2}}
3
x
9
2
y
2
1
\newline
3
x
9
2
y
2
3 x^{\frac{9}{2}} y^{2}
3
x
2
9
y
2
Get tutor help
Given
x
>
0
x>0
x
>
0
and
y
>
0
y>0
y
>
0
, select the expression that is equivalent to
\newline
256
x
16
y
12
4
\sqrt[4]{256 x^{16} y^{12}}
4
256
x
16
y
12
\newline
64
x
1
4
y
1
3
64 x^{\frac{1}{4}} y^{\frac{1}{3}}
64
x
4
1
y
3
1
\newline
64
x
4
y
3
64 x^{4} y^{3}
64
x
4
y
3
\newline
4
x
4
y
3
4 x^{4} y^{3}
4
x
4
y
3
\newline
4
x
1
4
y
1
3
4 x^{\frac{1}{4}} y^{\frac{1}{3}}
4
x
4
1
y
3
1
Get tutor help
Given
x
>
0
x>0
x
>
0
and
y
>
0
y>0
y
>
0
, select the expression that is equivalent to
\newline
81
x
2
y
18
4
\sqrt[4]{81 x^{2} y^{18}}
4
81
x
2
y
18
\newline
9
x
8
y
72
9 x^{8} y^{72}
9
x
8
y
72
\newline
9
x
1
2
y
9
2
9 x^{\frac{1}{2}} y^{\frac{9}{2}}
9
x
2
1
y
2
9
\newline
3
x
8
y
72
3 x^{8} y^{72}
3
x
8
y
72
\newline
3
x
1
2
y
9
2
3 x^{\frac{1}{2}} y^{\frac{9}{2}}
3
x
2
1
y
2
9
Get tutor help
Given
x
>
0
x>0
x
>
0
and
y
>
0
y>0
y
>
0
, select the expression that is equivalent to
\newline
256
x
8
y
10
4
\sqrt[4]{256 x^{8} y^{10}}
4
256
x
8
y
10
\newline
64
x
4
y
6
64 x^{4} y^{6}
64
x
4
y
6
\newline
4
x
2
y
5
2
4 x^{2} y^{\frac{5}{2}}
4
x
2
y
2
5
\newline
4
x
4
y
6
4 x^{4} y^{6}
4
x
4
y
6
\newline
64
x
2
y
5
2
64 x^{2} y^{\frac{5}{2}}
64
x
2
y
2
5
Get tutor help
Given
x
>
0
x>0
x
>
0
and
y
>
0
y>0
y
>
0
, select the expression that is equivalent to
\newline
81
x
6
y
10
4
\sqrt[4]{81 x^{6} y^{10}}
4
81
x
6
y
10
\newline
9
x
3
2
y
5
2
9 x^{\frac{3}{2}} y^{\frac{5}{2}}
9
x
2
3
y
2
5
\newline
3
x
2
3
y
2
5
3 x^{\frac{2}{3}} y^{\frac{2}{5}}
3
x
3
2
y
5
2
\newline
3
x
3
2
y
5
2
3 x^{\frac{3}{2}} y^{\frac{5}{2}}
3
x
2
3
y
2
5
\newline
9
x
2
3
y
2
5
9 x^{\frac{2}{3}} y^{\frac{2}{5}}
9
x
3
2
y
5
2
Get tutor help
Factor the following expression completely.
\newline
x
4
−
6
x
3
+
5
x
2
−
16
x
2
+
96
x
−
80
x^{4}-6 x^{3}+5 x^{2}-16 x^{2}+96 x-80
x
4
−
6
x
3
+
5
x
2
−
16
x
2
+
96
x
−
80
\newline
Answer:
Get tutor help
Factor the following expression completely.
\newline
x
4
−
6
x
3
−
7
x
2
−
9
x
2
+
54
x
+
63
x^{4}-6 x^{3}-7 x^{2}-9 x^{2}+54 x+63
x
4
−
6
x
3
−
7
x
2
−
9
x
2
+
54
x
+
63
\newline
Answer:
Get tutor help
Factor the following expression completely.
\newline
x
4
−
4
x
2
−
7
x
3
+
28
x
+
10
x
2
−
40
x^{4}-4 x^{2}-7 x^{3}+28 x+10 x^{2}-40
x
4
−
4
x
2
−
7
x
3
+
28
x
+
10
x
2
−
40
\newline
Answer:
Get tutor help
Factor the following expression completely.
\newline
x
4
−
16
x
2
+
3
x
3
−
48
x
+
2
x
2
−
32
x^{4}-16 x^{2}+3 x^{3}-48 x+2 x^{2}-32
x
4
−
16
x
2
+
3
x
3
−
48
x
+
2
x
2
−
32
\newline
Answer:
Get tutor help
Factor the following expression completely.
\newline
x
4
−
x
3
−
90
x
2
−
x
2
+
x
+
90
x^{4}-x^{3}-90 x^{2}-x^{2}+x+90
x
4
−
x
3
−
90
x
2
−
x
2
+
x
+
90
\newline
Answer:
Get tutor help
Factor the following expression completely.
\newline
x
4
−
16
x
2
−
5
x
3
+
80
x
−
6
x
2
+
96
x^{4}-16 x^{2}-5 x^{3}+80 x-6 x^{2}+96
x
4
−
16
x
2
−
5
x
3
+
80
x
−
6
x
2
+
96
\newline
Answer:
Get tutor help
Factor the following expression completely.
\newline
x
4
+
2
x
3
−
3
x
2
−
25
x
2
−
50
x
+
75
x^{4}+2 x^{3}-3 x^{2}-25 x^{2}-50 x+75
x
4
+
2
x
3
−
3
x
2
−
25
x
2
−
50
x
+
75
\newline
Answer:
Get tutor help
Factor the following expression completely.
\newline
x
4
−
16
x
2
−
x
3
+
16
x
−
2
x
2
+
32
x^{4}-16 x^{2}-x^{3}+16 x-2 x^{2}+32
x
4
−
16
x
2
−
x
3
+
16
x
−
2
x
2
+
32
\newline
Answer:
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Factor the following expression completely.
\newline
x
4
−
8
x
3
+
7
x
2
−
9
x
2
+
72
x
−
63
x^{4}-8 x^{3}+7 x^{2}-9 x^{2}+72 x-63
x
4
−
8
x
3
+
7
x
2
−
9
x
2
+
72
x
−
63
\newline
Answer:
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Factor the following expression completely.
\newline
x
4
+
3
x
3
+
2
x
2
−
16
x
2
−
48
x
−
32
x^{4}+3 x^{3}+2 x^{2}-16 x^{2}-48 x-32
x
4
+
3
x
3
+
2
x
2
−
16
x
2
−
48
x
−
32
\newline
Answer:
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Factor the following expression completely.
\newline
x
4
−
16
x
2
+
5
x
3
−
80
x
+
4
x
2
−
64
x^{4}-16 x^{2}+5 x^{3}-80 x+4 x^{2}-64
x
4
−
16
x
2
+
5
x
3
−
80
x
+
4
x
2
−
64
\newline
Answer:
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Factor the following expression completely.
\newline
x
4
−
4
x
3
−
12
x
2
−
4
x
2
+
16
x
+
48
x^{4}-4 x^{3}-12 x^{2}-4 x^{2}+16 x+48
x
4
−
4
x
3
−
12
x
2
−
4
x
2
+
16
x
+
48
\newline
Answer:
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Factor the following expression completely.
\newline
x
4
−
4
x
2
+
8
x
3
−
32
x
−
9
x
2
+
36
x^{4}-4 x^{2}+8 x^{3}-32 x-9 x^{2}+36
x
4
−
4
x
2
+
8
x
3
−
32
x
−
9
x
2
+
36
\newline
Answer:
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Factor the following expression completely.
\newline
x
4
−
9
x
2
−
6
x
3
+
54
x
+
8
x
2
−
72
x^{4}-9 x^{2}-6 x^{3}+54 x+8 x^{2}-72
x
4
−
9
x
2
−
6
x
3
+
54
x
+
8
x
2
−
72
\newline
Answer:
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Factor the following expression completely.
\newline
x
4
+
3
x
3
+
2
x
2
−
9
x
2
−
27
x
−
18
x^{4}+3 x^{3}+2 x^{2}-9 x^{2}-27 x-18
x
4
+
3
x
3
+
2
x
2
−
9
x
2
−
27
x
−
18
\newline
Answer:
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Factor the following expression completely.
\newline
x
4
+
9
x
3
−
10
x
2
−
9
x
2
−
81
x
+
90
x^{4}+9 x^{3}-10 x^{2}-9 x^{2}-81 x+90
x
4
+
9
x
3
−
10
x
2
−
9
x
2
−
81
x
+
90
\newline
Answer:
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Factor the following expression completely.
\newline
x
4
−
3
x
3
+
2
x
2
−
9
x
2
+
27
x
−
18
x^{4}-3 x^{3}+2 x^{2}-9 x^{2}+27 x-18
x
4
−
3
x
3
+
2
x
2
−
9
x
2
+
27
x
−
18
\newline
Answer:
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Factor the following expression completely.
\newline
x
4
+
x
3
−
42
x
2
−
x
2
−
x
+
42
x^{4}+x^{3}-42 x^{2}-x^{2}-x+42
x
4
+
x
3
−
42
x
2
−
x
2
−
x
+
42
\newline
Answer:
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Factor
27
t
3
−
125
v
3
27 t^{3}-125 v^{3}
27
t
3
−
125
v
3
completely.
\newline
Answer:
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Factor completely:
\newline
16
c
4
−
42
c
2
b
3
−
49
b
6
16 c^{4}-42 c^{2} b^{3}-49 b^{6}
16
c
4
−
42
c
2
b
3
−
49
b
6
\newline
Answer:
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Factor completely:
\newline
25
x
2
(
4
x
2
−
5
)
−
4
(
4
x
2
−
5
)
25 x^{2}\left(4 x^{2}-5\right)-4\left(4 x^{2}-5\right)
25
x
2
(
4
x
2
−
5
)
−
4
(
4
x
2
−
5
)
\newline
Answer:
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Factor completely:
\newline
25
x
2
(
2
x
2
−
5
)
−
16
(
2
x
2
−
5
)
25 x^{2}\left(2 x^{2}-5\right)-16\left(2 x^{2}-5\right)
25
x
2
(
2
x
2
−
5
)
−
16
(
2
x
2
−
5
)
\newline
Answer:
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Rewrite the expression as a product of four linear factors:
\newline
(
x
2
−
3
x
)
2
−
14
(
x
2
−
3
x
)
+
40
\left(x^{2}-3 x\right)^{2}-14\left(x^{2}-3 x\right)+40
(
x
2
−
3
x
)
2
−
14
(
x
2
−
3
x
)
+
40
\newline
Answer:
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