High voltage transmission lines can carry power without a neutral wire because they use the earth as a neutral, but in your house you can be damn sure the neutral is carrying power. Cut off the neutral blade on your appliance if you want to check it out.

"Electric power in watts produced by an electric current I consisting of a charge of Q coulombs every t seconds passing through an electric potential (voltage) difference of V is

P = work done per unit time = VQ/t = VI

Note that V is the "electric potential difference" and it take two conductors to supply power.