[tex]\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad
\sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}
\\\\\\
a^{-{ n}} \implies \cfrac{1}{a^{ n}}\qquad \qquad
\cfrac{1}{a^{ n}}\implies a^{-{ n}}\\\\
-----------------------------\\\\[/tex]
[tex]\bf (8a^{-3})^{-\frac{2}{3}}\qquad 8=2^3\implies (2^3a^{-3})^{-\frac{2}{3}}
\\\\\\
\textit{now, let's distribute the exponent}
\\\\\\
2^{\cfrac{}{}3\left( -\frac{2}{3} \right) }a^{-3\left( -\frac{2}{3} \right) }\implies 2^{-2}a^2\implies \cfrac{1}{2^2}\cdot a^2\implies \cfrac{a^2}{4}[/tex]
