[tex]\bf \begin{array}{llll} \textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{8em} \end{array} \begin{array}{llll} \textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf \left( 3t^{\frac{1}{6}} \right)^3 (2t^0)^{-3}\implies \left( 3^3 t^{\frac{1}{6}\cdot 3} \right) (2(1))^{-3}\implies \left( 27t^{\frac{1}{2}} \right) 2^{-3}\implies \cfrac{27t^{\frac{1}{2}}}{2^3} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \cfrac{27\sqrt{t}}{8}~\hfill[/tex]
