This is a case of indices
[tex]\begin{gathered} (\frac{1}{\sqrt[]{y}})^{-\frac{1}{5}} \\ =(\frac{1}{y^{\frac{1}{2}}})^{-\frac{1}{5}} \\ =y^{-\frac{1}{2}\times-\frac{1}{5}} \\ =y^{\frac{1}{10}} \\ =\sqrt[10]{y} \end{gathered}[/tex]
The third option is the right answer.
