Concepts: Power Law. A power law is a relationship in which a relative change in one quantity gives rise to a proportional relative change in the other quantity, independent of the initial size of those quantities.An example is the area of a square region in terms of the length of its side.oncepts: Power Law. A power law is a relationship in which a relative change in one quantity gives rise to a proportional relative change in the other quantity, independent of the initial size of those quantities. An example is the area of a square region in terms of the length of its side.