
theorem Th1:
  for a,b being Real, c being Nat holds
    (a / b) to_power c = (a to_power c) / (b to_power c)
  proof
    let a,b be Real;
    let c be Nat;
    (a / b) to_power c = (a*(1/b)) |^ c by XCMPLX_1:99
    .= a to_power c * (1/b) |^ c by NEWTON:7
    .= a to_power c * (1/ b |^ c) by PREPOWER:7
    .= (a to_power c) / (b |^ c) by XCMPLX_1:99;
    hence thesis;
  end;
