$\begin{align}  & x=\sqrt[13]{{{\sqrt{3}}^{10}}}\Rightarrow x={{3}^{\frac{10}{26}}}\,\,(*) \\  & {{x}^{2}}\times \sqrt[5]{{{x}^{2}}}\times \sqrt{{{x}^{3}}}={{x}^{2}}\times {{x}^{\frac{2}{5}}}\times {{x}^{\frac{3}{2}}}={{x}^{2+\frac{2}{5}+\frac{3}{2}}}={{x}^{\frac{39}{10}}}\xrightarrow{(*)}{{({{3}^{\frac{10}{26}}})}^{\frac{39}{10}}}={{3}^{\frac{10}{26}\times \frac{39}{10}}}={{3}^{\frac{39}{26}}}={{3}^{\frac{3}{2}}}\xrightarrow{mazjor}{{({{3}^{\frac{3}{2}}})}^{2}}={{3}^{3}}=27 \\ \end{align}$