Power in = power out holds only for transformers, because the primary and secondary are coupled by the core so they have to react at the same time. It does not hold for anything else, for example when you recharge a car battery the charger could be just a few watts, but when you crank the enging the power will be hundreds of watts.
The only rule that holds universally is energy in = energy out, that´s why it is called conservation of energy, not power or voltage or current. And because power=energy/time the power in power out holds in some cases, but not all.