[tex]\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad
\sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}\\\\
-------------------------------\\\\
\sqrt{x}\cdot \sqrt[5]{x}\implies \sqrt[2]{x^1}\cdot \sqrt[5]{x^1}\implies x^{\frac{1}{2}}\cdot x^{\frac{1}{5}}\impliedby
\begin{array}{llll}
\textit{same base, thus}\\
\textit{add the exponents}
\end{array}
\\\\\\
x^{\frac{1}{2}+\frac{1}{5}}\implies x^{\frac{5+2}{10}}\implies x^{\frac{7}{10}}[/tex]
