Which of the following is greatest ?

(2)^{\(\frac{1}{2}\)}  (3)^{\(\frac{1}{3}\)}  (4)^{\(\frac{1}{4}\)}  (6)^{\(\frac{1}{6}\)}

 Make the power equals to check the biggest value:

a) (2⁶)^{\(\frac{1}{2\;×\;6}\)} = (64)^{\(\frac{1}{12}\)}

b) (3⁴)^{\(\frac{1}{3\;×\;4}\)} = (81)^{\(\frac{1}{12}\)}

c)  (4³)^{\(\frac{1}{4 × 3}\)} = (64)^{\(\frac{1}{12}\)}

d) (6²)^{\(\frac{1}{6\;×\;2}\)}  = (36)^{\(\frac{1}{12}\)} 

Here,

Option (b) : 3\(\sqrt {3}\) is the biggest value.