[tex]\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad
\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}}}
\\ \quad \\ \quad \\
% radical denominator
\cfrac{1}{\sqrt[{ m}]{a^{ n}}}= \cfrac{1}{a^{\frac{{ n}}{{ m}}}}\implies a^{-\frac{{ n}}{{ m}}}\qquad thus\\
----------------------------\\
\\ \quad \\
[/tex][tex]\bf
\\ \quad \\
\cfrac{1}{x^{-\frac{3}{6}}}\implies \cfrac{1}{x^{-\frac{1}{2}}}\implies \cfrac{1}{\frac{1}{x\frac{1}{2}}}\implies \cfrac{1}{1}\cdot \cfrac{x^{\frac{1}{2}}}{1}
\\ \quad \\
x^{\frac{1}{2}}\implies \sqrt{x}[/tex]
