theorem Th5:
a >= 0 & b >= 0 & c > 0 implies (a*b) to_power c = a to_power c * b to_power c
proof
   assume that
A1: a >= 0 & b >= 0 and
A2: c > 0;
   now assume A3: a = 0 or b = 0; then
    (a*b) to_power c = 0 by A2,POWER:def 2;
    hence (a*b) to_power c = a to_power c * b to_power c by A3;
   end;
   hence thesis by A1,POWER:30;
end;
