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