[tex]\bf ~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \left( \sqrt{3} \right)\left( \sqrt[5]{3} \right)\implies \left( \sqrt[2]{3^1} \right)\left( \sqrt[5]{3^1} \right)\implies 3^{\frac{1}{2}}\cdot 3^{\frac{1}{5}}\implies 3^{\frac{1}{2}+\frac{1}{5}}\implies 3^{\frac{5+2}{10}}\implies 3^{\frac{7}{10}}[/tex]
