[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}[/tex]
[tex]\bf \left( \sqrt{5} \right)\left( \sqrt[3]{5} \right)\implies \left( \sqrt[2]{5^1} \right)\left( \sqrt[3]{5^1} \right)\implies 5^{\frac{1}{2}}\cdot 5^{\frac{1}{3}}\implies 5^{\frac{1}{2}+\frac{1}{3}}\qquad \impliedby \stackrel{LCD}{6} \\\\\\ 5^{\frac{(3)1+(2)1}{6}}\implies 5^{\frac{5}{6}}[/tex]
