Usually, the power set of an n-element set is denoted by 2^n, as power set will have 2^n elements.
Eg.: Take a finite set of elements, A = {1,2,3}. Here n = 3 (number of elements in the set). Then power set of A would be {{},{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}}. That is there would be 2^3 number of elements in the power set of A. Remember power set of A is set of subsets of A.
In general, for a set of n elements, the number of elements in its power set would be 2^n. The logic behind being, for each element we have a choice of selecting it or not i.e., 2 choices. We have n elements, therefore 2^n choices and 2^n subsets.
But here we have countably infinite set Σ* and its power set is denoted by 2^ Σ*. Such kind of denotation of power set can also be observed in NFA definition.