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Let’s check out your problem:
Which expression is equivalent to
\newline
(
a
3
)
6
(a^{3})^{6}
(
a
3
)
6
?
\newline
A.
a
729
a^{729}
a
729
\newline
B.
a
18
a^{18}
a
18
\newline
C.
a
9
a^9
a
9
\newline
D.
a
2
a^2
a
2
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Math Problems
Algebra 2
Evaluate rational exponents
Full solution
Q.
Which expression is equivalent to
\newline
(
a
3
)
6
(a^{3})^{6}
(
a
3
)
6
?
\newline
A.
a
729
a^{729}
a
729
\newline
B.
a
18
a^{18}
a
18
\newline
C.
a
9
a^9
a
9
\newline
D.
a
2
a^2
a
2
Identify base and exponent:
Identify the base and the exponent in the expression
(
a
3
)
6
(a^{3})^{6}
(
a
3
)
6
.
\newline
In
(
a
3
)
6
(a^{3})^{6}
(
a
3
)
6
, the base is
a
3
a^{3}
a
3
, and the outer exponent is
6
6
6
.
Apply power of 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
(
a
3
)
6
=
a
3
∗
6
(a^{3})^{6} = a^{3*6}
(
a
3
)
6
=
a
3
∗
6
Multiply exponents:
Multiply the exponents to simplify the expression.
\newline
3
×
6
=
18
3 \times 6 = 18
3
×
6
=
18
\newline
So,
(
a
3
)
6
=
a
18
(a^{3})^{6} = a^{18}
(
a
3
)
6
=
a
18
Check answer choices:
Check the answer choices to see which one matches the simplified expression.
\newline
The correct answer is B.
a
18
a^{18}
a
18
.
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or
A
B
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A
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B
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\newline
w
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w
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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
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\newline
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\newline
(
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A
A
A
or
A
B
\frac{A}{B}
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, where
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A
A
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\newline
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\newline
x
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4
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4
1
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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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