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Let’s check out your problem:
Solve for
n
n
n
:
(
−
7
5
)
11
(\frac{-7}{5})^{11}
(
5
−
7
)
11
÷
÷
÷
(
−
7
5
)
3
(\frac{-7}{5})^{3}
(
5
−
7
)
3
=
=
=
(
−
7
5
)
2
n
+
2
(\frac{-7}{5})^{2n+2}
(
5
−
7
)
2
n
+
2
View step-by-step help
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Math Problems
Algebra 1
Multiplication with rational exponents
Full solution
Q.
Solve for
n
n
n
:
(
−
7
5
)
11
(\frac{-7}{5})^{11}
(
5
−
7
)
11
÷
÷
÷
(
−
7
5
)
3
(\frac{-7}{5})^{3}
(
5
−
7
)
3
=
=
=
(
−
7
5
)
2
n
+
2
(\frac{-7}{5})^{2n+2}
(
5
−
7
)
2
n
+
2
Simplify Expression:
Step
1
1
1
: Simplify the expression using the properties of exponents.
\newline
(
−
7
5
)
11
÷
(
−
7
5
)
3
=
(
−
7
5
)
11
−
3
(-\frac{7}{5})^{11} \div (-\frac{7}{5})^{3} = (-\frac{7}{5})^{11-3}
(
−
5
7
)
11
÷
(
−
5
7
)
3
=
(
−
5
7
)
11
−
3
\newline
=
(
−
7
5
)
8
(-\frac{7}{5})^{8}
(
−
5
7
)
8
Set Equal and Solve:
Step
2
2
2
: Set the simplified expression equal to the given expression and solve for
n
n
n
.
(
−
7
5
)
8
=
(
−
7
5
)
2
n
+
2
\left(\frac{-7}{5}\right)^{8} = \left(\frac{-7}{5}\right)^{2n+2}
(
5
−
7
)
8
=
(
5
−
7
)
2
n
+
2
8
=
2
n
+
2
8 = 2n + 2
8
=
2
n
+
2
Final Solution:
Step
3
3
3
: Solve for
n
n
n
.
\newline
8
−
2
=
2
n
8 - 2 = 2n
8
−
2
=
2
n
\newline
6
=
2
n
6 = 2n
6
=
2
n
\newline
n
=
6
2
n = \frac{6}{2}
n
=
2
6
\newline
n
=
3
n = 3
n
=
3
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or
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\newline
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Write your answer in the form
A
A
A
or
A
B
\frac{A}{B}
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, where
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and
B
B
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are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.
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\newline
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\newline
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x
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Write your answer in the form
A
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A
or
A
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\frac{A}{B}
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A
, where
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A
A
and
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\newline
______
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