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To evaluate the equation \( 6^{(1/2)} \cdot (\sqrt{6})^3 = 36 \), let's simplify the left side step by step.
1. First, recall that \(\sqrt{6} = 6^{1/2}\). Therefore, \((\sqrt{6})^3 = (6^{1/2})^3\).
2. According to the Power of a Power Property \((a^m)^n = a^{m \cdot n}\), we can rewrite \((\sqrt{6})^3\) as:
\[
(6^{1/2})^3 = 6^{(1/2) \cdot 3} = 6^{3/2}
\]
3. Now, we have:
\[
6^{(1/2)} \cdot 6^{(3/2)}
\]
4. According to the Product Property \(a^m \cdot a^n = a^{m+n}\), we can combine the exponents:
\[
6^{(1/2) + (3/2)} = 6^{(1/2 + 3/2)} = 6^{4/2} = 6^2
\]
5. Simplifying \(6^2\) gives us:
\[
6^2 = 36
\]
Thus, the original statement is true: \(6^{(1/2)} \cdot (\sqrt{6})^3 = 36\).
The correct response is: **True, according to the Power of a Power Property.**