Is the equation 6^1/2⋅(√6)^3=36 true or false? Select the response that correctly answers the question and provides the appropriate justification.(1 point)

To evaluate the equation \( 6^{1/2} \cdot (\sqrt{6})^3 = 36 \), let's simplify each side step by step.

First, we know that:

\[
6^{1/2} = \sqrt{6}
\]

Next, we can rewrite \( (\sqrt{6})^3 \):

\[
(\sqrt{6})^3 = (6^{1/2})^3 = 6^{(1/2) \cdot 3} = 6^{3/2}
\]

Now, we can substitute these into the left-hand side of the equation:

\[
\sqrt{6} \cdot (\sqrt{6})^3 = 6^{1/2} \cdot 6^{3/2}
\]

Using the Product Property of exponents, which states \( a^m \cdot a^n = a^{m+n} \), we can add the exponents:

\[
6^{1/2} \cdot 6^{3/2} = 6^{(1/2 + 3/2)} = 6^{4/2} = 6^2
\]

And since:

\[
6^2 = 36
\]

So the equation:

\[
6^{1/2} \cdot (\sqrt{6})^3 = 36
\]

is true.

Thus, the correct response is:

**True, according to the Product Property.**