  We establish the solvability criteria for the equation $x^q=a$ in the field
of $p$-adic numbers, for any $q$ in two cases:
  (i) $q$ is not divisible by $p$; (ii) $q=p$. Using these criteria we show
that any $p$-adic number can be represented in finitely many different forms
and we describe the algorithms to obtain the corresponding representations.
Moreover it is showed that solvability problem of $x^q=a$ for any $q$ can be
reduced to the cases (i) and (ii).
