solve the equation 5 indice x = 1 and 16 indice x =0.165

Answer 1

incidentally, indices is the plural of index. "indice" is not a word.

By 5 index x do you mean 5 times the square root, or the 5th root?

If 5√x = 1 then √x = 1/5 and x = 1/25
If fifth root(x) = 1, then x = 1^5 = 1

similarly for the other problem.