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