question_answer

If \[{{\left[ \sqrt{\mathbf{2}}{{\left( \mathbf{1}{{\mathbf{6}}^{\mathbf{1/4}}}\mathbf{+777}{{\mathbf{6}}^{\mathbf{1/5}}} \right)}^{\mathbf{4}}} \right]}^{\mathbf{n}}}\mathbf{=4}\sqrt{\mathbf{2}}\], then find value of n.

A)  \[\frac{1}{4}\]                                                             

B)  \[\frac{1}{6}\]

C)  \[\frac{1}{5}\]             

D)  \[\frac{1}{3}\]

E)  None of these