If $${{\text{x}}^{\frac{1}{6}}} = {{\text{y}}^{\frac{2}{3}}},$$  then relation between x and y is.

Solution (By Examveda Team)

$$\eqalign{ & {{\text{x}}^{\frac{1}{6}}} = {{\text{y}}^{\frac{2}{3}}} \cr & \therefore {\text{LCM of }}\left( {3\,\& \,6} \right) = 6 \cr & \Rightarrow {{\text{x}}^{\frac{1}{6} \times 6}} = {{\text{y}}^{\frac{2}{3} \times 6}} \cr & \Rightarrow \boxed{{\text{x}} = {{\text{y}}^4}} \cr} $$