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Math Problems
Algebra 1
Multiplication with rational exponents
Select the equivalent expression.
\newline
(
b
8
b
4
)
1
2
\left(\frac{b^{8}}{b^{4}}\right)^{\frac{1}{2}}
(
b
4
b
8
)
2
1
\newline
1
b
2
\frac{1}{b^{2}}
b
2
1
\newline
b
2
b^{2}
b
2
\newline
1
b
\frac{1}{\sqrt{b}}
b
1
\newline
b
\sqrt{b}
b
Get tutor help
Select the equivalent expression.
\newline
a
−
6
⋅
a
−
3
18
\sqrt[18]{a^{-6} \cdot a^{-3}}
18
a
−
6
⋅
a
−
3
\newline
a
2
a^{2}
a
2
\newline
a
1
2
a^{\frac{1}{2}}
a
2
1
\newline
a
−
1
2
a^{-\frac{1}{2}}
a
−
2
1
\newline
a
−
2
a^{-2}
a
−
2
Get tutor help
Select the equivalent expression.
\newline
(
1
a
−
6
⋅
a
3
)
5
3
\left(\frac{1}{a^{-6} \cdot a^{3}}\right)^{\frac{5}{3}}
(
a
−
6
⋅
a
3
1
)
3
5
\newline
a
5
a^{5}
a
5
\newline
1
a
5
\frac{1}{a^{5}}
a
5
1
\newline
1
a
5
\frac{1}{\sqrt[5]{a}}
5
a
1
\newline
a
5
\sqrt[5]{a}
5
a
Get tutor help
Select the equivalent expression.
\newline
(
t
−
2
⋅
t
7
)
3
20
\left(t^{-2} \cdot t^{7}\right)^{\frac{3}{20}}
(
t
−
2
⋅
t
7
)
20
3
\newline
1
t
3
4
\frac{1}{\sqrt[4]{t^{3}}}
4
t
3
1
\newline
t
4
3
\sqrt[3]{t^{4}}
3
t
4
\newline
1
t
4
3
\frac{1}{\sqrt[3]{t^{4}}}
3
t
4
1
\newline
t
3
4
\sqrt[4]{t^{3}}
4
t
3
Get tutor help
Select the equivalent expression.
\newline
s
−
1
s
−
6
10
\sqrt[10]{\frac{s^{-1}}{s^{-6}}}
10
s
−
6
s
−
1
\newline
s
−
1
2
s^{-\frac{1}{2}}
s
−
2
1
\newline
s
−
2
s^{-2}
s
−
2
\newline
s
1
2
s^{\frac{1}{2}}
s
2
1
\newline
s
2
s^{2}
s
2
Get tutor help
Select the equivalent expression.
\newline
h
4
h
−
5
15
\sqrt[15]{\frac{h^{4}}{h^{-5}}}
15
h
−
5
h
4
\newline
h
−
5
3
h^{-\frac{5}{3}}
h
−
3
5
\newline
h
5
3
h^{\frac{5}{3}}
h
3
5
\newline
h
−
3
5
h^{-\frac{3}{5}}
h
−
5
3
\newline
h
3
5
h^{\frac{3}{5}}
h
5
3
Get tutor help
Select the equivalent expression.
\newline
(
1
k
−
8
⋅
k
5
)
5
3
\left(\frac{1}{k^{-8} \cdot k^{5}}\right)^{\frac{5}{3}}
(
k
−
8
⋅
k
5
1
)
3
5
\newline
1
k
5
\frac{1}{k^{5}}
k
5
1
\newline
k
5
k^{5}
k
5
\newline
1
k
5
\frac{1}{\sqrt[5]{k}}
5
k
1
\newline
k
5
\sqrt[5]{k}
5
k
Get tutor help
Select the equivalent expression.
\newline
(
t
t
7
)
5
24
\left(\frac{t}{t^{7}}\right)^{\frac{5}{24}}
(
t
7
t
)
24
5
\newline
t
5
4
\sqrt[4]{t^{5}}
4
t
5
\newline
t
4
5
\sqrt[5]{t^{4}}
5
t
4
\newline
1
t
4
5
\frac{1}{\sqrt[5]{t^{4}}}
5
t
4
1
\newline
1
t
5
4
\frac{1}{\sqrt[4]{t^{5}}}
4
t
5
1
Get tutor help
Select the equivalent expression.
\newline
(
r
−
7
r
4
)
3
11
\left(\frac{r^{-7}}{r^{4}}\right)^{\frac{3}{11}}
(
r
4
r
−
7
)
11
3
\newline
1
r
3
\frac{1}{\sqrt[3]{r}}
3
r
1
\newline
1
r
3
\frac{1}{r^{3}}
r
3
1
\newline
r
3
\sqrt[3]{r}
3
r
\newline
r
3
r^{3}
r
3
Get tutor help
Select the equivalent expression.
\newline
(
r
7
⋅
r
−
8
)
1
4
\left(r^{7} \cdot r^{-8}\right)^{\frac{1}{4}}
(
r
7
⋅
r
−
8
)
4
1
\newline
r
4
r^{4}
r
4
\newline
r
4
\sqrt[4]{r}
4
r
\newline
1
r
4
\frac{1}{\sqrt[4]{r}}
4
r
1
\newline
1
r
4
\frac{1}{r^{4}}
r
4
1
Get tutor help
Select the equivalent expression.
\newline
t
−
8
⋅
t
14
\sqrt[14]{t^{-8} \cdot t}
14
t
−
8
⋅
t
\newline
t
1
2
t^{\frac{1}{2}}
t
2
1
\newline
t
2
t^{2}
t
2
\newline
t
−
1
2
t^{-\frac{1}{2}}
t
−
2
1
\newline
t
−
2
t^{-2}
t
−
2
Get tutor help
Select the equivalent expression.
\newline
1
d
−
7
⋅
d
21
\sqrt[21]{\frac{1}{d^{-7} \cdot d}}
21
d
−
7
⋅
d
1
\newline
d
2
7
d^{\frac{2}{7}}
d
7
2
\newline
d
7
2
d^{\frac{7}{2}}
d
2
7
\newline
d
−
7
2
d^{-\frac{7}{2}}
d
−
2
7
\newline
d
−
2
7
d^{-\frac{2}{7}}
d
−
7
2
Get tutor help
Select the equivalent expression.
\newline
(
n
−
5
n
)
5
24
\left(\frac{n^{-5}}{n}\right)^{\frac{5}{24}}
(
n
n
−
5
)
24
5
\newline
1
n
5
4
\frac{1}{\sqrt[4]{n^{5}}}
4
n
5
1
\newline
n
4
5
\sqrt[5]{n^{4}}
5
n
4
\newline
n
5
4
\sqrt[4]{n^{5}}
4
n
5
\newline
1
n
4
5
\frac{1}{\sqrt[5]{n^{4}}}
5
n
4
1
Get tutor help
Select the equivalent expression.
\newline
y
−
7
y
−
5
4
\sqrt[4]{\frac{y^{-7}}{y^{-5}}}
4
y
−
5
y
−
7
\newline
y
1
2
y^{\frac{1}{2}}
y
2
1
\newline
y
2
y^{2}
y
2
\newline
y
−
1
2
y^{-\frac{1}{2}}
y
−
2
1
\newline
y
−
2
y^{-2}
y
−
2
Get tutor help
Select the equivalent expression.
\newline
(
x
−
8
⋅
x
−
5
)
4
13
\left(x^{-8} \cdot x^{-5}\right)^{\frac{4}{13}}
(
x
−
8
⋅
x
−
5
)
13
4
\newline
x
4
x^{4}
x
4
\newline
1
x
4
\frac{1}{x^{4}}
x
4
1
\newline
1
x
4
\frac{1}{\sqrt[4]{x}}
4
x
1
\newline
x
4
\sqrt[4]{x}
4
x
Get tutor help
Select the equivalent expression.
\newline
(
n
−
2
⋅
n
−
8
)
3
10
\left(n^{-2} \cdot n^{-8}\right)^{\frac{3}{10}}
(
n
−
2
⋅
n
−
8
)
10
3
\newline
n
3
n^{3}
n
3
\newline
n
3
\sqrt[3]{n}
3
n
\newline
1
n
3
\frac{1}{\sqrt[3]{n}}
3
n
1
\newline
1
n
3
\frac{1}{n^{3}}
n
3
1
Get tutor help
Select the expression that is equivalent to
1
(
6
x
)
3
2
\frac{1}{(6 x)^{\frac{3}{2}}}
(
6
x
)
2
3
1
\newline
(
6
x
)
3
\sqrt{(6 x)^{3}}
(
6
x
)
3
\newline
1
(
6
x
)
3
\frac{1}{\sqrt{(6 x)^{3}}}
(
6
x
)
3
1
\newline
(
6
x
)
2
3
\sqrt[3]{(6 x)^{2}}
3
(
6
x
)
2
\newline
1
(
6
x
)
2
3
\frac{1}{\sqrt[3]{(6 x)^{2}}}
3
(
6
x
)
2
1
Get tutor help
Select the expression that is equivalent to
1
(
3
x
+
1
)
5
4
\frac{1}{(3 x+1)^{\frac{5}{4}}}
(
3
x
+
1
)
4
5
1
\newline
1
(
3
x
+
1
)
5
4
\frac{1}{\sqrt[4]{(3 x+1)^{5}}}
4
(
3
x
+
1
)
5
1
\newline
1
(
3
x
+
1
)
4
5
\frac{1}{\sqrt[5]{(3 x+1)^{4}}}
5
(
3
x
+
1
)
4
1
\newline
(
3
x
+
1
)
5
4
\sqrt[4]{(3 x+1)^{5}}
4
(
3
x
+
1
)
5
\newline
(
3
x
+
1
)
4
5
\sqrt[5]{(3 x+1)^{4}}
5
(
3
x
+
1
)
4
Get tutor help
Select the expression that is equivalent to
2
x
3
2
2 x^{\frac{3}{2}}
2
x
2
3
\newline
2
x
3
\sqrt{2 x^{3}}
2
x
3
\newline
2
x
2
3
\sqrt[3]{2 x^{2}}
3
2
x
2
\newline
2
x
2
3
2 \sqrt[3]{x^{2}}
2
3
x
2
\newline
2
x
3
2 \sqrt{x^{3}}
2
x
3
Get tutor help
Select the expression that is equivalent to
(
5
x
)
−
1
2
(5 x)^{-\frac{1}{2}}
(
5
x
)
−
2
1
\newline
(
5
x
)
2
\sqrt{(5 x)^{2}}
(
5
x
)
2
\newline
1
(
5
x
)
2
\frac{1}{\sqrt{(5 x)^{2}}}
(
5
x
)
2
1
\newline
5
x
\sqrt{5 x}
5
x
\newline
1
5
x
\frac{1}{\sqrt{5 x}}
5
x
1
Get tutor help
Select the expression that is equivalent to
(
7
x
)
−
1
3
(7 x)^{-\frac{1}{3}}
(
7
x
)
−
3
1
\newline
1
(
7
x
)
3
\frac{1}{\sqrt{(7 x)^{3}}}
(
7
x
)
3
1
\newline
1
7
x
3
\frac{1}{\sqrt[3]{7 x}}
3
7
x
1
\newline
(
7
x
)
3
\sqrt{(7 x)^{3}}
(
7
x
)
3
\newline
7
x
3
\sqrt[3]{7 x}
3
7
x
Get tutor help
Select the expression that is equivalent to
6
x
4
3
6 x^{\frac{4}{3}}
6
x
3
4
\newline
6
x
3
4
\sqrt[4]{6 x^{3}}
4
6
x
3
\newline
6
x
3
4
6 \sqrt[4]{x^{3}}
6
4
x
3
\newline
6
x
4
3
\sqrt[3]{6 x^{4}}
3
6
x
4
\newline
6
x
4
3
6 \sqrt[3]{x^{4}}
6
3
x
4
Get tutor help
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
2
5
\frac{1}{\sqrt[5]{6 x^{2}}}
5
6
x
2
1
\newline
1
6
x
5
\frac{1}{6 \sqrt{x^{5}}}
6
x
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}{6 \sqrt[5]{x^{2}}}
6
5
x
2
1
Get tutor help
Select the expression that is equivalent to
1
(
2
x
2
+
7
)
1
2
\frac{1}{\left(2 x^{2}+7\right)^{\frac{1}{2}}}
(
2
x
2
+
7
)
2
1
1
\newline
1
(
2
x
2
+
7
)
2
\frac{1}{\sqrt{\left(2 x^{2}+7\right)^{2}}}
(
2
x
2
+
7
)
2
1
\newline
1
2
x
2
+
7
\frac{1}{\sqrt{2 x^{2}+7}}
2
x
2
+
7
1
\newline
(
2
x
2
+
7
)
2
\sqrt{\left(2 x^{2}+7\right)^{2}}
(
2
x
2
+
7
)
2
\newline
2
x
2
+
7
\sqrt{2 x^{2}+7}
2
x
2
+
7
Get tutor help
Select the expression that is equivalent to
1
(
7
x
)
4
3
\frac{1}{(7 x)^{\frac{4}{3}}}
(
7
x
)
3
4
1
\newline
1
(
7
x
)
4
3
\frac{1}{\sqrt[3]{(7 x)^{4}}}
3
(
7
x
)
4
1
\newline
(
7
x
)
4
3
\sqrt[3]{(7 x)^{4}}
3
(
7
x
)
4
\newline
1
(
7
x
)
3
4
\frac{1}{\sqrt[4]{(7 x)^{3}}}
4
(
7
x
)
3
1
\newline
(
7
x
)
3
4
\sqrt[4]{(7 x)^{3}}
4
(
7
x
)
3
Get tutor help
Select the expression that is equivalent to
1
(
2
x
)
5
2
\frac{1}{(2 x)^{\frac{5}{2}}}
(
2
x
)
2
5
1
\newline
1
(
2
x
)
5
\frac{1}{\sqrt{(2 x)^{5}}}
(
2
x
)
5
1
\newline
(
2
x
)
2
5
\sqrt[5]{(2 x)^{2}}
5
(
2
x
)
2
\newline
(
2
x
)
5
\sqrt{(2 x)^{5}}
(
2
x
)
5
\newline
1
(
2
x
)
2
5
\frac{1}{\sqrt[5]{(2 x)^{2}}}
5
(
2
x
)
2
1
Get tutor help
Select the expression that is equivalent to
1
(
5
x
)
2
3
\frac{1}{(5 x)^{\frac{2}{3}}}
(
5
x
)
3
2
1
\newline
(
5
x
)
2
3
\sqrt[3]{(5 x)^{2}}
3
(
5
x
)
2
\newline
(
5
x
)
3
\sqrt{(5 x)^{3}}
(
5
x
)
3
\newline
1
(
5
x
)
3
\frac{1}{\sqrt{(5 x)^{3}}}
(
5
x
)
3
1
\newline
1
(
5
x
)
2
3
\frac{1}{\sqrt[3]{(5 x)^{2}}}
3
(
5
x
)
2
1
Get tutor help
Select the expression that is equivalent to
1
(
2
x
)
−
1
3
\frac{1}{(2 x)^{-\frac{1}{3}}}
(
2
x
)
−
3
1
1
\newline
1
2
x
3
\frac{1}{\sqrt[3]{2 x}}
3
2
x
1
\newline
2
x
3
\sqrt[3]{2 x}
3
2
x
\newline
(
2
x
)
3
\sqrt{(2 x)^{3}}
(
2
x
)
3
\newline
1
(
2
x
)
3
\frac{1}{\sqrt{(2 x)^{3}}}
(
2
x
)
3
1
Get tutor help
Select the expression that is equivalent to
1
(
2
x
2
+
3
)
−
3
5
\frac{1}{\left(2 x^{2}+3\right)^{-\frac{3}{5}}}
(
2
x
2
+
3
)
−
5
3
1
\newline
(
2
x
2
+
3
)
5
3
\sqrt[3]{\left(2 x^{2}+3\right)^{5}}
3
(
2
x
2
+
3
)
5
\newline
1
(
2
x
2
+
3
)
5
3
\frac{1}{\sqrt[3]{\left(2 x^{2}+3\right)^{5}}}
3
(
2
x
2
+
3
)
5
1
\newline
(
2
x
2
+
3
)
3
5
\sqrt[5]{\left(2 x^{2}+3\right)^{3}}
5
(
2
x
2
+
3
)
3
\newline
1
(
2
x
2
+
3
)
3
5
\frac{1}{\sqrt[5]{\left(2 x^{2}+3\right)^{3}}}
5
(
2
x
2
+
3
)
3
1
Get tutor help
Express the following fraction in simplest form, only using positive exponents.
\newline
−
3
(
u
−
4
)
2
6
a
−
9
\frac{-3\left(u^{-4}\right)^{2}}{6 a^{-9}}
6
a
−
9
−
3
(
u
−
4
)
2
\newline
Answer:
Get tutor help
Express the following fraction in simplest form, only using positive exponents.
\newline
15
u
10
q
−
6
(
−
3
u
4
q
3
)
3
\frac{15 u^{10} q^{-6}}{\left(-3 u^{4} q^{3}\right)^{3}}
(
−
3
u
4
q
3
)
3
15
u
10
q
−
6
\newline
Answer:
Get tutor help
Express the following fraction in simplest form, only using positive exponents.
\newline
6
x
2
t
(
−
2
x
−
3
t
4
)
5
\frac{6 x^{2} t}{\left(-2 x^{-3} t^{4}\right)^{5}}
(
−
2
x
−
3
t
4
)
5
6
x
2
t
\newline
Answer:
Get tutor help
Express the following fraction in simplest form, only using positive exponents.
\newline
(
3
k
3
v
2
)
−
5
4
k
7
v
5
\frac{\left(3 k^{3} v^{2}\right)^{-5}}{4 k^{7} v^{5}}
4
k
7
v
5
(
3
k
3
v
2
)
−
5
\newline
Answer:
Get tutor help
Express the following fraction in simplest form, only using positive exponents.
\newline
(
3
a
−
1
t
3
)
−
2
12
a
\frac{\left(3 a^{-1} t^{3}\right)^{-2}}{12 a}
12
a
(
3
a
−
1
t
3
)
−
2
\newline
Answer:
Get tutor help
Express the following fraction in simplest form, only using positive exponents.
\newline
15
r
9
(
3
j
−
2
r
5
)
−
1
\frac{15 r^{9}}{\left(3 j^{-2} r^{5}\right)^{-1}}
(
3
j
−
2
r
5
)
−
1
15
r
9
\newline
Answer:
Get tutor help
Express the following fraction in simplest form, only using positive exponents.
\newline
−
2
(
t
3
)
−
3
10
t
2
b
6
\frac{-2\left(t^{3}\right)^{-3}}{10 t^{2} b^{6}}
10
t
2
b
6
−
2
(
t
3
)
−
3
\newline
Answer:
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Express the following fraction in simplest form, only using positive exponents.
\newline
(
5
m
5
r
−
3
)
−
2
2
r
9
\frac{\left(5 m^{5} r^{-3}\right)^{-2}}{2 r^{9}}
2
r
9
(
5
m
5
r
−
3
)
−
2
\newline
Answer:
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Express the following fraction in simplest form, only using positive exponents.
\newline
−
3
(
x
)
−
2
15
x
5
\frac{-3(x)^{-2}}{15 x^{5}}
15
x
5
−
3
(
x
)
−
2
\newline
Answer:
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Express the following fraction in simplest form, only using positive exponents.
\newline
4
j
−
9
w
8
(
2
w
2
)
−
4
\frac{4 j^{-9} w^{8}}{\left(2 w^{2}\right)^{-4}}
(
2
w
2
)
−
4
4
j
−
9
w
8
\newline
Answer:
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Express the following fraction in simplest form, only using positive exponents.
\newline
3
c
5
t
−
5
(
−
4
t
5
)
4
\frac{3 c^{5} t^{-5}}{\left(-4 t^{5}\right)^{4}}
(
−
4
t
5
)
4
3
c
5
t
−
5
\newline
Answer:
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Express the following fraction in simplest form, only using positive exponents.
\newline
6
d
−
5
u
−
6
(
3
d
−
5
u
5
)
−
1
\frac{6 d^{-5} u^{-6}}{\left(3 d^{-5} u^{5}\right)^{-1}}
(
3
d
−
5
u
5
)
−
1
6
d
−
5
u
−
6
\newline
Answer:
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Express the following fraction in simplest form, only using positive exponents.
\newline
4
(
d
−
4
q
−
1
)
2
4
d
10
q
−
2
\frac{4\left(d^{-4} q^{-1}\right)^{2}}{4 d^{10} q^{-2}}
4
d
10
q
−
2
4
(
d
−
4
q
−
1
)
2
\newline
Answer:
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Express the following fraction in simplest form, only using positive exponents.
\newline
2
(
p
−
3
b
5
)
−
2
3
b
−
2
\frac{2\left(p^{-3} b^{5}\right)^{-2}}{3 b^{-2}}
3
b
−
2
2
(
p
−
3
b
5
)
−
2
\newline
Answer:
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Express the following fraction in simplest form, only using positive exponents.
\newline
2
(
u
−
2
h
−
1
)
−
1
6
u
−
9
h
9
\frac{2\left(u^{-2} h^{-1}\right)^{-1}}{6 u^{-9} h^{9}}
6
u
−
9
h
9
2
(
u
−
2
h
−
1
)
−
1
\newline
Answer:
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Express the following fraction in simplest form, only using positive exponents.
\newline
(
4
a
−
5
k
−
4
)
−
5
2
k
−
9
\frac{\left(4 a^{-5} k^{-4}\right)^{-5}}{2 k^{-9}}
2
k
−
9
(
4
a
−
5
k
−
4
)
−
5
\newline
Answer:
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Express the following fraction in simplest form, only using positive exponents.
\newline
3
(
b
−
4
)
3
15
b
−
7
j
−
5
\frac{3\left(b^{-4}\right)^{3}}{15 b^{-7} j^{-5}}
15
b
−
7
j
−
5
3
(
b
−
4
)
3
\newline
Answer:
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Express the following fraction in simplest form, only using positive exponents.
\newline
6
j
−
7
n
−
2
(
3
j
5
)
4
\frac{6 j^{-7} n^{-2}}{\left(3 j^{5}\right)^{4}}
(
3
j
5
)
4
6
j
−
7
n
−
2
\newline
Answer:
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Express the following fraction in simplest form, only using positive exponents.
\newline
3
y
10
−
3
(
w
)
5
\frac{3 y^{10}}{-3(w)^{5}}
−
3
(
w
)
5
3
y
10
\newline
Answer:
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Express the following fraction in simplest form using only positive exponents.
\newline
3
k
(
3
k
4
)
5
\frac{3 k}{\left(3 k^{4}\right)^{5}}
(
3
k
4
)
5
3
k
\newline
Answer:
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Express the following fraction in simplest form using only positive exponents.
\newline
2
m
9
(
4
m
5
)
4
\frac{2 m^{9}}{\left(4 m^{5}\right)^{4}}
(
4
m
5
)
4
2
m
9
\newline
Answer:
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