[tex]\bf a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n}
\qquad \qquad
\sqrt[ m]{a^ n}\implies a^{\frac{ n}{ m}}\\\\
-------------------------------\\\\
\left( 5^{\frac{4}{5}} \right)^6\implies 5^{\frac{4}{5}\cdot 6}\implies 5^{\frac{24}{5}}\implies \sqrt[5]{5^{24}}~~
\begin{cases}
5^{24}=5^{5+5+5+5+4}\\
\qquad 5^5\cdot 5^5\cdot 5^5\cdot 5^5\cdot 5^4\\
\qquad (5^4)^5 5^4
\end{cases}
\\\\\\
\sqrt[5]{(5^4)^5 \cdot 5^4}\implies (5^4)\sqrt[5]{5^4}\implies 625\sqrt[5]{625}[/tex]
