question_answer

What are the possible solutions for x in the equation \[{{x}^{\sqrt{x}}}=\sqrt[n]{{{x}^{x}}},\] where x and n are positive integers?

A)  0, n                             

B)  1, n

C)  \[n,\,\,{{n}^{2}}\]                  

D)  \[1,\,\,{{n}^{2}}\]

E)  None of these