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Let’s check out your problem:
Select the answer which is equivalent to the given expression using your calculator.
\newline
(
−
6
a
)
2
(
5
b
)
4
\frac{(-6 a)^{2}}{(5 b)^{4}}
(
5
b
)
4
(
−
6
a
)
2
\newline
a
=
−
5
and
b
=
−
6
a=-5 \text { and } b=-6
a
=
−
5
and
b
=
−
6
\newline
1
900
\frac{1}{900}
900
1
\newline
1
1800
\frac{1}{1800}
1800
1
\newline
−
1
900
-\frac{1}{900}
−
900
1
\newline
−
1
1800
-\frac{1}{1800}
−
1800
1
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Home
Math Problems
Algebra 1
Multiplication with rational exponents
Full solution
Q.
Select the answer which is equivalent to the given expression using your calculator.
\newline
(
−
6
a
)
2
(
5
b
)
4
\frac{(-6 a)^{2}}{(5 b)^{4}}
(
5
b
)
4
(
−
6
a
)
2
\newline
a
=
−
5
and
b
=
−
6
a=-5 \text { and } b=-6
a
=
−
5
and
b
=
−
6
\newline
1
900
\frac{1}{900}
900
1
\newline
1
1800
\frac{1}{1800}
1800
1
\newline
−
1
900
-\frac{1}{900}
−
900
1
\newline
−
1
1800
-\frac{1}{1800}
−
1800
1
Substitute values:
Substitute the given values of
a
a
a
and
b
b
b
into the expression.
(
−
6
a
)
2
(
5
b
)
4
\frac{(-6a)^{2}}{(5b)^{4}}
(
5
b
)
4
(
−
6
a
)
2
with
a
=
−
5
a = -5
a
=
−
5
and
b
=
−
6
b = -6
b
=
−
6
becomes
(
−
6
∗
(
−
5
)
)
2
(
5
∗
(
−
6
)
)
4
\frac{(-6*(-5))^{2}}{(5*(-6))^{4}}
(
5
∗
(
−
6
)
)
4
(
−
6
∗
(
−
5
)
)
2
.
Calculate values:
Calculate the value of
(
−
6
∗
(
−
5
)
)
(-6*(-5))
(
−
6
∗
(
−
5
))
and
(
5
∗
(
−
6
)
)
(5*(-6))
(
5
∗
(
−
6
))
.
−
6
×
−
5
=
30
-6 \times -5 = 30
−
6
×
−
5
=
30
and
5
×
−
6
=
−
30
5 \times -6 = -30
5
×
−
6
=
−
30
.
Raise to powers:
Raise the results to the respective powers.
\newline
(
30
)
2
(30)^{2}
(
30
)
2
and
(
−
30
)
4
(-30)^{4}
(
−
30
)
4
.
Calculate powers:
Calculate the powers.
3
0
2
=
900
30^2 = 900
3
0
2
=
900
and
(
−
30
)
4
=
810000
(-30)^4 = 810000
(
−
30
)
4
=
810000
.
Divide results:
Divide the results.
900
810000
.
\frac{900}{810000}.
810000
900
.
Simplify division:
Simplify the division.
900
/
810000
=
1
/
900
900 / 810000 = 1 / 900
900/810000
=
1/900
.
Check sign:
Check the sign of the result.
\newline
Since both the numerator and the denominator are positive, the result is positive.
More problems from Multiplication with rational exponents
Question
Simplify.
\newline
8
1
1
2
81^{\frac{1}{2}}
8
1
2
1
\newline
_____________
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Posted 1 year ago
Question
Simplify.
\newline
(
−
32
)
1
/
5
(-32)^{1/5}
(
−
32
)
1/5
\newline
______
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Posted 1 year ago
Question
Simplify. Assume all variables are positive.
\newline
w
4
3
w
7
3
\frac{w^{\frac{4}{3}}}{w^{\frac{7}{3}}}
w
3
7
w
3
4
\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
______
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Posted 9 months ago
Question
Simplify. Assume all variables are positive.
\newline
(
2
r
1
3
)
8
(2r^{\frac{1}{3}})^8
(
2
r
3
1
)
8
\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
______
Get tutor help
Posted 9 months ago
Question
Simplify. Assume all variables are positive.
\newline
v
7
4
⋅
v
9
4
v^{\frac{7}{4}} \cdot v^{\frac{9}{4}}
v
4
7
⋅
v
4
9
\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
Get tutor help
Posted 9 months ago
Question
Simplify.
\newline
1
1
4
⋅
1
1
4
1^{\frac{1}{4}} \cdot 1^{\frac{1}{4}}
1
4
1
⋅
1
4
1
\newline
______
Get tutor help
Posted 9 months ago
Question
Simplify.
\newline
3
2
(
−
1
/
5
)
32^{(-1/5)}
3
2
(
−
1/5
)
Get tutor help
Posted 1 year ago
Question
Simplify. Assume all variables are positive.
\newline
w
3
2
w
5
2
\frac{w^{\frac{3}{2}}}{w^{\frac{5}{2}}}
w
2
5
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
Get tutor help
Posted 1 year ago
Question
Simplify. Assume all variables are positive.
\newline
(
27
x
)
2
3
(27x)^{\frac{2}{3}}
(
27
x
)
3
2
\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
______
Get tutor help
Posted 1 year ago
Question
Simplify. Assume all variables are positive.
\newline
x
1
4
x
11
4
\frac{x^{\frac{1}{4}}}{x^{\frac{11}{4}}}
x
4
11
x
4
1
\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
Get tutor help
Posted 1 year ago
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