[tex]\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \\\\\\
\sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}\\\\
-----------------------------\\\\
\textit{let's say you have }\qquad \sqrt[27]{64^9}
\\\\
\sqrt[27]{64^9}\implies 64^{\cfrac{}{}\frac{9}{27}}\quad \quad however\implies 64=4^3
\\\\
thus\qquad 64^{\cfrac{}{}\frac{9}{27}}\implies (4^3)^{\cfrac{}{}\frac{9}{27}}\implies
(4)^{\cfrac{}{}3\cdot \frac{9}{27}}\implies 4^{\cfrac{}{}\frac{9}{9}}\implies 4^1\implies 4[/tex]
