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.

$$6^{\frac{5}{3}}=(6^5)^{\frac{1}{3}}=(6^3)^\frac{1}{3}(6^2)^\frac{1}{3}=6(36)^\frac{1}{3}$$
