,
\frac{27* \sqrt3 * 81}{\sqrt[3]9 * \sqrt[5]{27}}=\frac{3^3* 3^{\frac{1}{2}} * 3^4}{3^{\frac{2}{3}} * 3^{\frac{3}{5}}}=
\frac{3^{7\frac{1}{2}}}{3^{\frac{10+9}{15}}}=\frac{3^{\frac{15}{2}}}{3^{\frac{19}{15}}}=
\frac{3^{\frac{225}{2}}}{3^{\frac{38}{30}}}=3^{\frac{225-38}{30}}=3^{\frac{187}{30}}