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Let’s check out your problem:
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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Math Problems
Algebra 1
Multiplication with rational exponents
Full solution
Q.
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:
Apply Negative Exponent Rule:
Apply the
negative exponent rule
which states that
a
−
n
=
1
a
n
a^{-n} = \frac{1}{a^n}
a
−
n
=
a
n
1
.
(
32
x
−
40
y
−
20
)
−
1
5
(32x^{-40}y^{-20})^{-\frac{1}{5}}
(
32
x
−
40
y
−
20
)
−
5
1
=
1
(
32
x
−
40
y
−
20
)
1
5
= \frac{1}{(32x^{-40}y^{-20})^{\frac{1}{5}}}
=
(
32
x
−
40
y
−
20
)
5
1
1
Apply Power of a Power Rule:
Apply the power of a power rule which states that
(
a
m
)
n
=
a
m
∗
n
(a^m)^n = a^{m*n}
(
a
m
)
n
=
a
m
∗
n
.
\newline
1
(
32
x
−
40
y
−
20
)
1
5
\frac{1}{(32x^{-40}y^{-20})^{\frac{1}{5}}}
(
32
x
−
40
y
−
20
)
5
1
1
\newline
=
1
3
2
1
5
×
x
−
40
×
(
1
5
)
×
y
−
20
×
(
1
5
)
\frac{1}{32^{\frac{1}{5}} \times x^{-40\times(\frac{1}{5})} \times y^{-20\times(\frac{1}{5})}}
3
2
5
1
×
x
−
40
×
(
5
1
)
×
y
−
20
×
(
5
1
)
1
Simplify Exponents:
Simplify the exponents by multiplying them with
1
5
\frac{1}{5}
5
1
.
1
(
3
2
1
5
⋅
x
−
8
⋅
y
−
4
)
\frac{1}{(32^{\frac{1}{5}} \cdot x^{-8} \cdot y^{-4})}
(
3
2
5
1
⋅
x
−
8
⋅
y
−
4
)
1
Simplify Fifth Root:
Simplify the fifth root of
32
32
32
.
3
2
1
/
5
32^{1/5}
3
2
1/5
is the same as the fifth root of
32
32
32
, which is
2
2
2
because
2
5
=
32
2^5 = 32
2
5
=
32
.
1
2
⋅
x
−
8
⋅
y
−
4
\frac{1}{2 \cdot x^{-8} \cdot y^{-4}}
2
⋅
x
−
8
⋅
y
−
4
1
Apply Negative Exponent Rule:
Apply the negative exponent rule again to move the
x
x
x
and
y
y
y
terms to the numerator.
\newline
1
2
⋅
x
−
8
⋅
y
−
4
\frac{1}{2 \cdot x^{-8} \cdot y^{-4}}
2
⋅
x
−
8
⋅
y
−
4
1
\newline
=
x
8
⋅
y
4
2
\frac{x^8 \cdot y^4}{2}
2
x
8
⋅
y
4
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A
or
A
B
\frac{A}{B}
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, where
A
A
A
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B
B
B
are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.
\newline
______
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\newline
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\newline
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w
2
3
\newline
\newline
Write your answer in the form
A
A
A
or
A
B
\frac{A}{B}
B
A
, where
A
A
A
and
B
B
B
are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.
\newline
______
\newline
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\newline
(
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)
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3
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)
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\newline
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A
A
A
or
A
B
\frac{A}{B}
B
A
, where
A
A
A
and
B
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\newline
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\newline
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4
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x
4
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x
4
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\newline
Write your answer in the form
A
A
A
or
A
B
\frac{A}{B}
B
A
, where
A
A
A
and
B
B
B
are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.
\newline
______
\newline
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