$\begin{align}
  & x=\sqrt[3]{{{(\sqrt[7]{3})}^{20}}}=\sqrt[3]{\sqrt[7]{{{3}^{20}}}}=\sqrt[21]{{{3}^{20}}}={{3}^{\frac{20}{21}}} \\
 & \left\{ \begin{matrix}
   \sqrt[5]{{{x}^{7}}}=\sqrt[5]{{{({{3}^{\frac{20}{21}}})}^{7}}}=\sqrt[5]{{{3}^{\frac{20\times 7}{21}}}}=\sqrt[5]{{{3}^{\frac{20}{3}}}}={{3}^{\frac{20}{3}\times \frac{1}{5}}}={{3}^{\frac{20}{15}}}={{3}^{\frac{4}{3}}}  \\
   \sqrt{x}=\sqrt{{{3}^{\frac{20}{21}}}}={{3}^{\frac{20}{21}\times \frac{1}{2}}}={{3}^{\frac{10}{21}}}  \\
   {{x}^{3}}={{({{3}^{\frac{20}{21}}})}^{3}}={{3}^{\frac{20\times 3}{21}}}={{3}^{\frac{20}{7}}}  \\
\end{matrix} \right. \\
 & \Rightarrow hasel=\frac{{{3}^{\frac{4}{3}}}\times {{3}^{\frac{10}{21}}}}{20}=\frac{{{3}^{\frac{28+10}{21}}}}{20}=\frac{{{3}^{\frac{38}{21}}}}{20}={{3}^{\frac{38}{21}-\frac{20}{7}}}={{3}^{\frac{38-60}{21}}}={{3}^{-\frac{22}{21}}} \\
\end{align}$