not sure I can read those exponents above, but in case it helps -> [tex]\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \\
\sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}
\\\quad \\\\
% rational negative exponent
a^{-\frac{{ n}}{{ m}}} =
\cfrac{1}{a^{\frac{{ n}}{{ m}}}} \implies \cfrac{1}{\sqrt[{ m}]{a^{ n}}}\qquad
\\\\\\
% radical denominator
\cfrac{1}{\sqrt[{ m}]{a^{ n}}}= \cfrac{1}{a^{\frac{{ n}}{{ m}}}}\implies a^{-\frac{{ n}}{{ m}}} [/tex]
