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.**