How does $6^{\frac{5}{3}}$ simplify to $6\sqrt[3]{36}$? I was recently given a problem along the lines of the below:

Simplify $6^{\frac{5}{3}}$ to an expression in the format $a\sqrt[b]{c}$.

The answer, $6\sqrt[3]{36}$, was then given to me before I could figure out the problem myself. I'm wondering what the steps to perform this simplification are, and how they work.

\begin{eqnarray*}
6^{5/3} &=& \left(6^5\right)^{1/3} \\ \\
&=& \left(6 \times 6 \times 6 \times 6 \times 6\right)^{1/3} \\ \\
&=& \left(6 \times 6 \times 6\right)^{1/3} \times \left(6 \times 6\right)^{1/3} \\ \\ &=& 6 \times \left(36\right)^{1/3} \\ \\
&=& 6 \times \sqrt[3]{36}
\end{eqnarray*}
