[tex]\bf a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n}
\qquad \qquad
\sqrt[ m]{a^ n}\implies a^{\frac{ n}{ m}}\\\\
-------------------------------[/tex]
[tex]\bf \left( \sqrt[4]{81} \right)^5\implies \sqrt[4]{81^5}\implies 81^{\frac{5}{4}}\quad \checkmark
\\\\\\
7^{\frac{5}{7}}\implies \sqrt[7]{7^5}\implies \left( \sqrt[7]{7} \right)^5\quad \otimes
\\\\\\
6^{\frac{2}{7}}\implies \sqrt[7]{6^2}\implies \left( \sqrt[7]{6} \right)^2\quad \otimes
\\\\\\
5^{\frac{3}{2}}\implies \sqrt[2]{5^3}\implies \left( \sqrt{5} \right)^3\quad \checkmark[/tex]
