Question

Write (8a^-3)^-2/3 in simplest form Please explain as if I were five years old

Answer 1

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

$\bf (8a^{-3})^{-\frac{2}{3}}\qquad 8=2^3\implies (2^3a^{-3})^{-\frac{2}{3}} \\\\\\ \textit{now, let's distribute the exponent} \\\\\\ 2^{\cfrac{}{}3\left( -\frac{2}{3} \right) }a^{-3\left( -\frac{2}{3} \right) }\implies 2^{-2}a^2\implies \cfrac{1}{2^2}\cdot a^2\implies \cfrac{a^2}{4}$