Mathematics, 21.06.2019 12:30 kevin7334
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![\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}](/tpl/images/0000/2440/49edd.png)
![\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}}](/tpl/images/0000/2440/7c8dd.png)
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