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Math Problems
Algebra 1
Multiplication with rational exponents
Given
x
>
0
x>0
x
>
0
, the expression
x
8
4
\sqrt[4]{x^{8}}
4
x
8
is equivalent to
\newline
x
x
x
\newline
x
x
2
4
x \sqrt[4]{x^{2}}
x
4
x
2
\newline
x
2
x
2
4
x^{2} \sqrt[4]{x^{2}}
x
2
4
x
2
\newline
x
2
x^{2}
x
2
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Given
x
>
0
x>0
x
>
0
, the expression
x
14
3
\sqrt[3]{x^{14}}
3
x
14
is equivalent to
\newline
x
4
x
2
3
x^{4} \sqrt[3]{x^{2}}
x
4
3
x
2
\newline
x
5
x
2
3
x^{5} \sqrt[3]{x^{2}}
x
5
3
x
2
\newline
x
4
x
3
3
x^{4} \sqrt[3]{x^{3}}
x
4
3
x
3
\newline
x
5
x
3
3
x^{5} \sqrt[3]{x^{3}}
x
5
3
x
3
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Given
x
>
0
x>0
x
>
0
, the expression
x
32
5
\sqrt[5]{x^{32}}
5
x
32
is equivalent to
\newline
x
6
x
2
5
x^{6} \sqrt[5]{x^{2}}
x
6
5
x
2
\newline
x
7
x
2
5
x^{7} \sqrt[5]{x^{2}}
x
7
5
x
2
\newline
x
7
x^{7}
x
7
\newline
x
6
x^{6}
x
6
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Given
x
>
0
x>0
x
>
0
, the expression
x
32
8
\sqrt[8]{x^{32}}
8
x
32
is equivalent to
\newline
x
5
x
6
8
x^{5} \sqrt[8]{x^{6}}
x
5
8
x
6
\newline
x
5
x^{5}
x
5
\newline
x
4
x
6
8
x^{4} \sqrt[8]{x^{6}}
x
4
8
x
6
\newline
x
4
x^{4}
x
4
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Given
x
>
0
x>0
x
>
0
, the expression
x
32
3
\sqrt[3]{x^{32}}
3
x
32
is equivalent to
\newline
x
10
x
3
x^{10} \sqrt[3]{x}
x
10
3
x
\newline
x
11
x
2
3
x^{11} \sqrt[3]{x^{2}}
x
11
3
x
2
\newline
x
11
x
3
x^{11} \sqrt[3]{x}
x
11
3
x
\newline
x
10
x
2
3
x^{10} \sqrt[3]{x^{2}}
x
10
3
x
2
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Given
x
>
0
x>0
x
>
0
, the expression
x
13
8
\sqrt[8]{x^{13}}
8
x
13
is equivalent to
\newline
x
2
x
4
8
x^{2} \sqrt[8]{x^{4}}
x
2
8
x
4
\newline
x
x
5
8
x \sqrt[8]{x^{5}}
x
8
x
5
\newline
x
x
4
8
x \sqrt[8]{x^{4}}
x
8
x
4
\newline
x
2
x
5
8
x^{2} \sqrt[8]{x^{5}}
x
2
8
x
5
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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
x
1
6
=
x
a
\frac{x^{4}}{x^{\frac{1}{6}}}=x^{a}
x
6
1
x
4
=
x
a
\newline
Answer:
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Select the expression that is equivalent to
5
x
−
5
4
5 x^{-\frac{5}{4}}
5
x
−
4
5
\newline
1
5
x
4
5
\frac{1}{\sqrt[5]{5 x^{4}}}
5
5
x
4
1
\newline
5
x
4
5
\frac{5}{\sqrt[5]{x^{4}}}
5
x
4
5
\newline
1
5
x
5
4
\frac{1}{\sqrt[4]{5 x^{5}}}
4
5
x
5
1
\newline
5
x
5
4
\frac{5}{\sqrt[4]{x^{5}}}
4
x
5
5
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Select the expression that is equivalent to
1
(
3
x
2
+
3
)
4
5
\frac{1}{\left(3 x^{2}+3\right)^{\frac{4}{5}}}
(
3
x
2
+
3
)
5
4
1
\newline
(
3
x
2
+
3
)
4
5
\sqrt[5]{\left(3 x^{2}+3\right)^{4}}
5
(
3
x
2
+
3
)
4
\newline
(
3
x
2
+
3
)
5
4
\sqrt[4]{\left(3 x^{2}+3\right)^{5}}
4
(
3
x
2
+
3
)
5
\newline
1
(
3
x
2
+
3
)
4
5
\frac{1}{\sqrt[5]{\left(3 x^{2}+3\right)^{4}}}
5
(
3
x
2
+
3
)
4
1
\newline
1
(
3
x
2
+
3
)
5
4
\frac{1}{\sqrt[4]{\left(3 x^{2}+3\right)^{5}}}
4
(
3
x
2
+
3
)
5
1
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Select the expression that is equivalent to
1
(
3
x
)
5
4
\frac{1}{(3 x)^{\frac{5}{4}}}
(
3
x
)
4
5
1
\newline
1
(
3
x
)
4
5
\frac{1}{\sqrt[5]{(3 x)^{4}}}
5
(
3
x
)
4
1
\newline
1
(
3
x
)
5
4
\frac{1}{\sqrt[4]{(3 x)^{5}}}
4
(
3
x
)
5
1
\newline
(
3
x
)
5
4
\sqrt[4]{(3 x)^{5}}
4
(
3
x
)
5
\newline
(
3
x
)
4
5
\sqrt[5]{(3 x)^{4}}
5
(
3
x
)
4
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Select the expression that is equivalent to
1
7
x
1
2
\frac{1}{7 x^{\frac{1}{2}}}
7
x
2
1
1
\newline
1
7
x
2
\frac{1}{7 \sqrt{x^{2}}}
7
x
2
1
\newline
1
7
x
2
\frac{1}{\sqrt{7 x^{2}}}
7
x
2
1
\newline
1
7
x
\frac{1}{\sqrt{7 x}}
7
x
1
\newline
1
7
x
\frac{1}{7 \sqrt{x}}
7
x
1
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Select the expression that is equivalent to
1
(
6
x
)
5
2
\frac{1}{(6 x)^{\frac{5}{2}}}
(
6
x
)
2
5
1
\newline
1
(
6
x
)
5
\frac{1}{\sqrt{(6 x)^{5}}}
(
6
x
)
5
1
\newline
1
(
6
x
)
2
5
\frac{1}{\sqrt[5]{(6 x)^{2}}}
5
(
6
x
)
2
1
\newline
(
6
x
)
5
\sqrt{(6 x)^{5}}
(
6
x
)
5
\newline
(
6
x
)
2
5
\sqrt[5]{(6 x)^{2}}
5
(
6
x
)
2
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Simplify the following expression to simplest form using only positive exponents.
\newline
(
64
x
−
3
y
−
15
)
4
3
\left(64 x^{-3} y^{-15}\right)^{\frac{4}{3}}
(
64
x
−
3
y
−
15
)
3
4
\newline
Answer:
\newline
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Simplify the following expression to simplest form using only positive exponents.
\newline
(
32
x
10
y
5
)
−
1
5
\left(32 x^{10} y^{5}\right)^{-\frac{1}{5}}
(
32
x
10
y
5
)
−
5
1
\newline
Answer:
\newline
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Simplify the following expression to simplest form using only positive exponents.
\newline
(
16
x
−
12
y
−
8
)
−
5
4
\left(16 x^{-12} y^{-8}\right)^{-\frac{5}{4}}
(
16
x
−
12
y
−
8
)
−
4
5
\newline
Answer:
\newline
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Simplify the following expression to simplest form using only positive exponents.
\newline
(
64
x
−
24
y
12
)
4
3
\left(64 x^{-24} y^{12}\right)^{\frac{4}{3}}
(
64
x
−
24
y
12
)
3
4
\newline
Answer:
\newline
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Simplify the following expression to simplest form using only positive exponents.
\newline
(
64
x
−
24
y
12
)
4
3
\left(64 x^{-24} y^{12}\right)^{\frac{4}{3}}
(
64
x
−
24
y
12
)
3
4
\newline
Answer:
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Simplify the following expression to simplest form using only positive exponents.
\newline
(
32
x
−
40
y
−
20
)
−
1
5
\left(32 x^{-40} y^{-20}\right)^{-\frac{1}{5}}
(
32
x
−
40
y
−
20
)
−
5
1
\newline
Answer:
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Simplify the following expression to simplest form using only positive exponents.
\newline
(
16
x
−
12
y
−
8
)
−
5
4
\left(16 x^{-12} y^{-8}\right)^{-\frac{5}{4}}
(
16
x
−
12
y
−
8
)
−
4
5
\newline
Answer:
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Simplify the following expression to simplest form using only positive exponents.
\newline
(
64
x
−
2
y
−
10
)
3
2
\left(64 x^{-2} y^{-10}\right)^{\frac{3}{2}}
(
64
x
−
2
y
−
10
)
2
3
\newline
Answer:
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Simplify the following expression to simplest form using only positive exponents.
\newline
(
100
x
−
4
y
2
)
−
5
2
\left(100 x^{-4} y^{2}\right)^{-\frac{5}{2}}
(
100
x
−
4
y
2
)
−
2
5
\newline
Answer:
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Simplify the following expression to simplest form using only positive exponents.
\newline
(
81
x
−
6
y
2
)
1
2
\left(81 x^{-6} y^{2}\right)^{\frac{1}{2}}
(
81
x
−
6
y
2
)
2
1
\newline
Answer:
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Simplify the following expression to simplest form using only positive exponents.
\newline
(
32
x
25
y
−
40
)
4
5
\left(32 x^{25} y^{-40}\right)^{\frac{4}{5}}
(
32
x
25
y
−
40
)
5
4
\newline
Answer:
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Simplify the following expression to simplest form using only positive exponents.
\newline
(
64
x
−
24
y
3
)
1
3
\left(64 x^{-24} y^{3}\right)^{\frac{1}{3}}
(
64
x
−
24
y
3
)
3
1
\newline
Answer:
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Simplify the following expression to simplest form using only positive exponents.
\newline
(
64
x
3
y
−
18
)
−
5
3
\left(64 x^{3} y^{-18}\right)^{-\frac{5}{3}}
(
64
x
3
y
−
18
)
−
3
5
\newline
Answer:
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Simplify the following expression to simplest form using only positive exponents.
\newline
(
100
x
12
y
−
14
)
−
1
2
\left(100 x^{12} y^{-14}\right)^{-\frac{1}{2}}
(
100
x
12
y
−
14
)
−
2
1
\newline
Answer:
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Simplify the following expression to simplest form using only positive exponents.
\newline
(
36
x
−
6
y
2
)
−
5
2
\left(36 x^{-6} y^{2}\right)^{-\frac{5}{2}}
(
36
x
−
6
y
2
)
−
2
5
\newline
Answer:
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Simplify the following expression to simplest form using only positive exponents.
\newline
(
125
x
3
y
−
6
)
1
3
\left(125 x^{3} y^{-6}\right)^{\frac{1}{3}}
(
125
x
3
y
−
6
)
3
1
\newline
Answer:
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Simplify the following expression to simplest form using only positive exponents.
\newline
(
32
x
20
y
−
25
)
−
2
5
\left(32 x^{20} y^{-25}\right)^{-\frac{2}{5}}
(
32
x
20
y
−
25
)
−
5
2
\newline
Answer:
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Simplify the following expression to simplest form using only positive exponents.
\newline
(
32
x
−
20
y
−
5
)
−
2
5
\left(32 x^{-20} y^{-5}\right)^{-\frac{2}{5}}
(
32
x
−
20
y
−
5
)
−
5
2
\newline
Answer:
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Simplify the following expression to simplest form using only positive exponents.
\newline
(
8
x
−
15
y
18
)
−
5
3
\left(8 x^{-15} y^{18}\right)^{-\frac{5}{3}}
(
8
x
−
15
y
18
)
−
3
5
\newline
Answer:
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Simplify the following expression to simplest form using only positive exponents.
\newline
(
32
x
5
y
−
40
)
−
3
5
\left(32 x^{5} y^{-40}\right)^{-\frac{3}{5}}
(
32
x
5
y
−
40
)
−
5
3
\newline
Answer:
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Simplify the following expression to simplest form using only positive exponents.
\newline
(
27
x
−
9
y
18
)
−
5
3
\left(27 x^{-9} y^{18}\right)^{-\frac{5}{3}}
(
27
x
−
9
y
18
)
−
3
5
\newline
Answer:
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Simplify the following expression to simplest form using only positive exponents.
\newline
(
81
x
16
y
−
12
)
−
5
4
\left(81 x^{16} y^{-12}\right)^{-\frac{5}{4}}
(
81
x
16
y
−
12
)
−
4
5
\newline
Answer:
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Simplify the following expression to simplest form using only positive exponents.
\newline
(
64
x
−
3
y
−
15
)
4
3
\left(64 x^{-3} y^{-15}\right)^{\frac{4}{3}}
(
64
x
−
3
y
−
15
)
3
4
\newline
Answer:
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Simplify the following expression to simplest form using only positive exponents.
\newline
(
64
x
−
18
y
21
)
5
3
\left(64 x^{-18} y^{21}\right)^{\frac{5}{3}}
(
64
x
−
18
y
21
)
3
5
\newline
Answer:
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Simplify the following expression to simplest form using only positive exponents.
\newline
(
9
x
8
y
−
12
)
−
1
2
\left(9 x^{8} y^{-12}\right)^{-\frac{1}{2}}
(
9
x
8
y
−
12
)
−
2
1
\newline
Answer:
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Express the following fraction in simplest form, only using positive exponents.
\newline
4
h
5
(
4
h
−
4
)
−
3
\frac{4 h^{5}}{\left(4 h^{-4}\right)^{-3}}
(
4
h
−
4
)
−
3
4
h
5
\newline
Answer:
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Express the following fraction in simplest form, only using positive exponents.
\newline
2
q
−
1
j
6
(
3
q
−
1
j
2
)
−
1
\frac{2 q^{-1} j^{6}}{\left(3 q^{-1} j^{2}\right)^{-1}}
(
3
q
−
1
j
2
)
−
1
2
q
−
1
j
6
\newline
Answer:
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Express the following fraction in simplest form, only using positive exponents.
\newline
(
4
x
−
5
k
3
)
−
5
12
x
−
6
k
−
8
\frac{\left(4 x^{-5} k^{3}\right)^{-5}}{12 x^{-6} k^{-8}}
12
x
−
6
k
−
8
(
4
x
−
5
k
3
)
−
5
\newline
Answer:
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Express the following fraction in simplest form, only using positive exponents.
\newline
12
m
−
7
y
−
9
(
4
m
5
)
−
1
\frac{12 m^{-7} y^{-9}}{\left(4 m^{5}\right)^{-1}}
(
4
m
5
)
−
1
12
m
−
7
y
−
9
\newline
Answer:
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Express the following fraction in simplest form, only using positive exponents.
\newline
4
d
−
4
v
−
8
(
3
d
4
)
3
\frac{4 d^{-4} v^{-8}}{\left(3 d^{4}\right)^{3}}
(
3
d
4
)
3
4
d
−
4
v
−
8
\newline
Answer:
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Select the equivalent expression.
\newline
b
−
8
b
−
6
8
\sqrt[8]{\frac{b^{-8}}{b^{-6}}}
8
b
−
6
b
−
8
\newline
b
−
4
b^{-4}
b
−
4
\newline
b
−
1
4
b^{-\frac{1}{4}}
b
−
4
1
\newline
b
1
4
b^{\frac{1}{4}}
b
4
1
\newline
b
4
b^{4}
b
4
Get tutor help
Select the equivalent expression.
\newline
s
−
7
⋅
s
2
15
\sqrt[15]{s^{-7} \cdot s^{2}}
15
s
−
7
⋅
s
2
\newline
s
1
3
s^{\frac{1}{3}}
s
3
1
\newline
s
−
1
3
s^{-\frac{1}{3}}
s
−
3
1
\newline
s
−
3
s^{-3}
s
−
3
\newline
s
3
s^{3}
s
3
Get tutor help
Select the equivalent expression.
\newline
(
t
6
t
−
2
)
1
14
\left(\frac{t^{6}}{t^{-2}}\right)^{\frac{1}{14}}
(
t
−
2
t
6
)
14
1
\newline
1
t
7
4
\frac{1}{\sqrt[4]{t^{7}}}
4
t
7
1
\newline
1
t
4
7
\frac{1}{\sqrt[7]{t^{4}}}
7
t
4
1
\newline
t
4
7
\sqrt[7]{t^{4}}
7
t
4
\newline
t
7
4
\sqrt[4]{t^{7}}
4
t
7
Get tutor help
Select the equivalent expression.
\newline
k
6
k
4
6
\sqrt[6]{\frac{k^{6}}{k^{4}}}
6
k
4
k
6
\newline
k
−
1
3
k^{-\frac{1}{3}}
k
−
3
1
\newline
k
−
3
k^{-3}
k
−
3
\newline
k
3
k^{3}
k
3
\newline
k
1
3
k^{\frac{1}{3}}
k
3
1
Get tutor help
Select the equivalent expression.
\newline
1
x
⋅
x
5
24
\sqrt[24]{\frac{1}{x \cdot x^{5}}}
24
x
⋅
x
5
1
\newline
x
−
1
4
x^{-\frac{1}{4}}
x
−
4
1
\newline
x
1
4
x^{\frac{1}{4}}
x
4
1
\newline
x
4
x^{4}
x
4
\newline
x
−
4
x^{-4}
x
−
4
Get tutor help
Select the equivalent expression.
\newline
1
k
−
7
⋅
k
−
5
30
\sqrt[30]{\frac{1}{k^{-7} \cdot k^{-5}}}
30
k
−
7
⋅
k
−
5
1
\newline
k
−
2
5
k^{-\frac{2}{5}}
k
−
5
2
\newline
k
−
5
2
k^{-\frac{5}{2}}
k
−
2
5
\newline
k
5
2
k^{\frac{5}{2}}
k
2
5
\newline
k
2
5
k^{\frac{2}{5}}
k
5
2
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Select the equivalent expression.
\newline
1
t
8
⋅
t
6
10
\sqrt[10]{\frac{1}{t^{8} \cdot t^{6}}}
10
t
8
⋅
t
6
1
\newline
t
−
7
5
t^{-\frac{7}{5}}
t
−
5
7
\newline
t
5
7
t^{\frac{5}{7}}
t
7
5
\newline
t
−
5
7
t^{-\frac{5}{7}}
t
−
7
5
\newline
t
7
5
t^{\frac{7}{5}}
t
5
7
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Select the equivalent expression.
\newline
(
s
−
8
s
7
)
1
6
\left(\frac{s^{-8}}{s^{7}}\right)^{\frac{1}{6}}
(
s
7
s
−
8
)
6
1
\newline
1
s
5
\frac{1}{\sqrt{s^{5}}}
s
5
1
\newline
s
2
5
\sqrt[5]{s^{2}}
5
s
2
\newline
1
s
2
5
\frac{1}{\sqrt[5]{s^{2}}}
5
s
2
1
\newline
s
5
\sqrt{s^{5}}
s
5
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