Question

I forgot how to do this

Answer 1

$\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad \sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}\\\\ a^{-{ n}} \implies \cfrac{1}{a^{ n}}\qquad \qquad \cfrac{1}{a^{ n}}\implies a^{-{ n}}$

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