question_answer

If \[{{\mathbf{a}}^{\mathbf{2}}}+\text{ }{{\mathbf{b}}^{\mathbf{2}}}+\text{ }{{\mathbf{c}}^{\mathbf{2}}}=\text{ }\mathbf{4abc}\], then find the value of \[{{\left[ {{\mathbf{4}}^{\frac{\mathbf{1}}{\mathbf{bc}}}} \right]}^{\mathbf{a}}}{{\left[ {{\mathbf{4}}^{\frac{\mathbf{1}}{\mathbf{ac}}}} \right]}^{\mathbf{b}}}{{\left[ {{\mathbf{4}}^{\frac{\mathbf{1}}{\mathbf{ab}}}} \right]}^{\mathbf{c}}}\] .

A) 5 abc

B)  4abc   

C)  64

D)  256

E)  None of these