[tex]\begin{array}{llll} \textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} \end{array} ~\hfill \begin{array}{llll} \textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\left(729x^3y^{-18} \right)^{\frac{1}{6}}\implies \left(3^6x^3y^{-18} \right)^{\frac{1}{6}}\implies \left(3^{6\cdot \frac{1}{6}}x^{3\cdot \frac{1}{6}}y^{-18\cdot \frac{1}{6}} \right) \\\\\\ 3^1x^{\frac{1}{2}}y^{-3}\implies 3\sqrt[2]{x^1}\cfrac{1}{y^3}\implies \cfrac{3\sqrt{x}}{y^3}[/tex]
