Question

Select the equivalent expression.
\[\left(3^2\cdot 5\right)^{3}=?\]
Choose 1 answer:
Choose 1 answer:
(Choice A)
\[3^5\cdot 5\]
A
\[3^5\cdot 5\]
(Choice B)
\[3^6\cdot 5^3\]
B
\[3^6\cdot 5^3\]
(Choice C)
\[3^6\cdot 5\]
C
\[3^6\cdot 5\]
(Choice D)
\[3^5\cdot 5^3\]
D
\[3^5\cdot 5^3\]

Answer 1

To simplify the expression \(\left(3^2 \cdot 5\right)^{3}\), we can use the property of exponents which states that \((ab)^n = a^n \cdot b^n\).

Applying this property, we have:

\[
\left(3^2 \cdot 5\right)^{3} = (3^2)^{3} \cdot (5)^{3}
\]

Now applying the rule \((a^m)^n = a^{m \cdot n}\):

\[
(3^2)^{3} = 3^{2 \cdot 3} = 3^6
\]
and
\[
(5)^{3} = 5^{3}
\]

Now, let's combine these results:

\[
(3^2 \cdot 5)^{3} = 3^6 \cdot 5^3
\]

So, the equivalent expression is:

\[
\boxed{B} \quad 3^6 \cdot 5^3
\]