reserve a,b,n for Element of NAT;

theorem Th8:
  for a, b be non zero Real holds
  (a*b) to_power n = a to_power n * b to_power n
proof
  let a, b be non zero Real;
A1: b #Z n = b to_power n by POWER:43;
  (a * b) #Z n = (a * b) to_power n & a #Z n = a to_power n by POWER:43;
  hence thesis by A1,PREPOWER:40;
end;
