[tex]a^{\frac{n}{m} = \sqrt[m]{a^n}}\\a^{-n} = (\frac1{a^n})\\\\3*27^{-\frac23}*81^{\frac34}=3*\frac{1}{27^{\frac23}} * \sqrt[4]{81^3}=3*\frac{1}{\sqrt[3]{27^2}}*\sqrt[4]{531441} = 3*\frac1{\sqrt[3]{729}} * \sqrt[4]{27*27*27*27}=3*\frac{1}{\sqrt[3]{9*9*9}}*27=3*\frac19*27=3*3=9[/tex]
[tex]4^3*81^{\frac14}*(\sqrt[5]{32})^{-1}=64*\sqrt[4]{81}*\frac{1}{\sqrt[5]{32}} = 64*3*\frac12=32*3=96[/tex]
