[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}\\\\ \sqrt[3]{8x^5y^7} \\\\[-0.35em] ~\dotfill\\\\ \sqrt[3]{8x^5y^7}\implies \sqrt[3]{2^3x^5y^7}\implies \left( 2^3x^5y^7 \right)^{\frac{1}{3}}\implies 2^{3\cdot \frac{1}{3}}x^{5\cdot \frac{1}{3}}y^{7\cdot \frac{1}{3}}\implies 2x^{\frac{5}{3}}y^{\frac{7}{3}}[/tex]
