[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[6]{x^5} \right)^7\implies \sqrt[6]{(x^5)^7}\implies \sqrt[6]{x^{5\cdot 7}}\implies \sqrt[6]{x^{35}}\implies x^{\frac{35}{6}}[/tex]
