The greatest among following numbers is : $${\left( 3 \right)^{\frac{1}{3}}},$$ $${\left( 2 \right)^{\frac{1}{2}}}$$ , 1, $${\left( 6 \right)^{\frac{1}{6}}}$$

Solution(By Examveda Team)

L.C.M. of powers (3, 2, 1 and 6) = 6
$$\eqalign{ & {\left( 3 \right)^{\frac{1}{3}}} \Rightarrow {\left( {{3^2}} \right)^{\frac{1}{6}}} = {{\bf{9}}^{\frac{{\bf{1}}}{{\bf{6}}}}} \cr & {\left( 2 \right)^{\frac{1}{2}}} \Rightarrow {\left( {{2^3}} \right)^{\frac{1}{6}}} = {8^{\frac{1}{6}}} \cr & (1) \Rightarrow {\left( {{1^6}} \right)^{\frac{1}{6}}} = {1^{\frac{1}{6}}} \cr & {\left( 6 \right)^{\frac{1}{6}}} \Rightarrow {\left( {{6^1}} \right)^{\frac{1}{6}}} = {6^{\frac{1}{6}}} \cr} $$