How to simplify square root $$
\sqrt[3]{a}(\sqrt[3]{a^2}-\sqrt[3]{a^5})
$$
How can this be simplified? I can't find anything for doing the subtraction.

*

*Distribute $\;\sqrt[\large 3]{a}\;$ over the difference, 

*use the property that $\;\sqrt[\large a]{b}\cdot \sqrt[\large a]{c} =
   \sqrt[\large a]{b\cdot c},\;$ and 

*remember that $\sqrt[\Large a]{b^a}    = b$


$$
\begin{align} \sqrt[\Large 3]{a}\left(\sqrt[\Large 3]{a^2}-\sqrt[\Large 3]{a^5}\right) & = \sqrt[\Large 3]{a}\cdot \sqrt[\Large 3]{a^2} - \sqrt[\Large 3]{a}\cdot \sqrt[\Large3]{a^5} \\ \\
& = \sqrt[\Large 3]{a\cdot a^2} - \sqrt[\Large a]{a\cdot a^5} \\ \\
& = \sqrt[\Large 3]{a^3} - \sqrt[\Large 3]{a^6} \\ \\ 
& = a - \sqrt[\Large 3]{(a^2)^3} \\ \\
& = a \;\;- \;\;a^2 \\ \\
&
\end{align}
$$
