Question

Please provide an explanation as well!
(g^2/3)^2 *g^-2

Answer 1

`\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^( n)} \qquad \qquad \sqrt[{ m}]{a^( n)}\implies a^{\frac{{ n}}{{ m}}} \\\\\\ \left.\qquad \qquad \right.\textit{negative exponents}\\\\ a^{-{ n}} \implies \cfrac{1}{a^( n)} \qquad \qquad \cfrac{1}{a^( n)}\implies a^{-{ n}} \qquad \qquad a^{{{ n}}}\implies \cfrac{1}{a^{-{{ n}}}}\\\\ -------------------------------`


`\bf \left( g^{(2)/(3)} \right)^2\cdot g^(-2)\implies \left( g^{(2)/(3)} \right)^2\cdot g^(-2)\implies \left( g^{(2)/(3)\cdot 2} \right)\cdot g^(-2)\implies g^{(4)/(3)}\cdot g^(-2) \\\\\\ g^{(4)/(3)-2}\implies g^{(4-6)/(3)}\implies g^{(-2)/(3)}\implies \cfrac{1}{g^{(2)/(3)}}\implies \cfrac{1}{\sqrt[3]{g^2}}`