The greatest among following numbers is : ( 3 )^1/3, ( 2 )^1/2 , 1, ( 6 )^1/6

Answer: Option D

L.C.M. of powers (3, 2, 1 and 6) = 6
$$\begin{array}{rl}& {\left(3\right)}^{\frac{1}{3}}\Rightarrow {\left(3^2\right)}^{\frac{1}{6}}=9^{\frac{1}{6}}\\ & {\left(2\right)}^{\frac{1}{2}}\Rightarrow {\left(2^3\right)}^{\frac{1}{6}}=8^{\frac{1}{6}}\\ & (1)\Rightarrow {\left(1^6\right)}^{\frac{1}{6}}=1^{\frac{1}{6}}\\ & {\left(6\right)}^{\frac{1}{6}}\Rightarrow {\left(6^1\right)}^{\frac{1}{6}}=6^{\frac{1}{6}}\end{array}$$