Return to power (idea)
This is true, but with a clarification which is glossed over in all but the most advanced courses.
For AC power, I and V are vector quantities, not scalar. The peak current may not be drawn at the same time as the potential difference peaks, especially if the load is reactive, rather than just resistive.
Imagine two sine waves which may or may not be out of phase with each other. If the waves are in phase, then our P=IV equation holds. If the waves are exactly out of phase, then P=0. However much power we supply, no work will get done. All electrical equipment has a power factor between these extremes, with motors generally being worse than solid-state equipment.
This power factor is very important in machines which use a large amount of electricity; but can generally be ignored on small equipment. A low power factor means that the power station has to supply current at times when potential is low, and can damage their equipment. For this reason, large factories have to measure and declare their power factor.
Electrical equipment may be rated in one or more ways.
W = PowerFactor × VA
If VA, but not the power factor is supplied, then we can still work out a worst-case heat dissipation; it will always be VA or better.
¹ Those who took Physics, at any rate.