[tex]\bf \sqrt[3]{x^2}\implies \left(\stackrel{outer~function}{\left( \stackrel{inner~function}{x} \right) }\right)^{\frac{2}{3}}\implies \stackrel{\qquad \qquad chain~rule}{\stackrel{outer}{\cfrac{2}{3}x^{-\frac{1}{3}}}}\cdot \stackrel{inner}{1}
\\\\\\
\cfrac{2}{3x^{\frac{1}{3}}}\implies \cfrac{2}{3\sqrt[3]{x}}[/tex]
so, the function is really a composite function, you could think of it
[tex]\bf \begin{cases}
f(x)=x\\
g(x)=x^{\frac{2}{3}}
\end{cases}\implies g(~~f(x)~~)=(x)^{\frac{2}{3}}[/tex]
