How does $6^{\frac{5}{3}}$ simplify to $6\sqrt[3]{36}$?

Question

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.

Answer 1

\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*}

Answer 2

$$6^{5/3} = 6^{1 + 2/3} = 6 \cdot 6^{2/3} = 6 \sqrt[3]{6^2}.$$

Answer 3

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