[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 -----------------------------\\\\
\left( -\cfrac{64}{125} \right)^{-\frac{5}{3}}\iff \left( -\cfrac{125}{64} \right)^{\frac{5}{3}}\implies \left[ \left( -\cfrac{125}{64} \right)^{\frac{1}{3}}\right]^{\frac{5}{1}}
\\\\\\
\left[ \sqrt[3]{\cfrac{-125}{64}} \right]^5\implies \left[ \cfrac{-5}{4} \right]^5\implies \cfrac{(-5)^5}{(4)^5}\implies \cfrac{-3125}{1024}[/tex]
