to the risk of sounding a bit redundant.
[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 \sqrt[3]{\sqrt[4]{a^9b^3}}\implies \sqrt[3]{(a^9b^3)^{\frac{1}{4}}}\implies \left[ (a^9b^3)^{\frac{1}{4}} \right]^{\frac{1}{3}}\implies (a^9b^3)^{\frac{1}{4}\cdot \frac{1}{3}}
\\\\\\
(a^9b^3)^{\frac{1}{12}}\implies a^{9\cdot \frac{1}{12}}b^{3\cdot \frac{1}{12}}\implies a^{\frac{3}{4}}b^{\frac{1}{4}}\implies \sqrt[4]{a^3}\cdot \sqrt[4]{b^1}
\\\\\\
\sqrt[4]{a^3b^1}\implies \sqrt[4]{a^3b} [/tex]
