theorem Th35:
  EXP(k) is multiplicative
proof
  for n,m being non zero Nat st n,m are_coprime holds (
  EXP(k)).(n*m) = (EXP(k)).n * (EXP(k)).m
  proof
    let n,m be non zero Nat;
    assume n,m are_coprime;
    thus (EXP(k)).(n*m) = (n*m)|^k by Def1
      .= n|^k * m|^k by NEWTON:7
      .= (EXP(k)).n * m|^k by Def1
      .= (EXP(k)).n * (EXP(k)).m by Def1;
  end;
  hence EXP(k) is multiplicative;
end;
