reserve G for Group,
  a,b for Element of G,
  m, n for Nat,
  p for Prime;

theorem
  a |^ b is p-power implies a is p-power
proof
  assume a |^ b is p-power;
  then consider r be Nat such that
A1: ord (a |^ b) = p |^ r;
  ord a = p |^ r by A1,Th6;
  hence thesis;
end;
