TeX source:
\begin{array}{ccl} \sqrt[3]{x} \cdot \sqrt{x} &=& x^{\frac{1}{3}} \cdot x^{\frac{1}{2}} \cr &=& x^{\frac{1}{3} + \frac{1}{2}} \cr &=& x^{\frac{5}{6}} \cr &=& \sqrt [6]{x^5} \end{array}