the.com/power set

means The power set of a set is the collection of ALL its possible subsets — from the empty set to the whole thing itself — and if the original set has n elements, the power set has exactly 2^n of them.

from From 'power' in its mathematical sense of exponentiation — the term tracks directly to the fact that a set of n elements yields exactly 2^n subsets, so 'power set' names the set of subsets by naming the operation that counts them. 'Set' itself enters mathematical English in the late 1800s via set theory's founders, notably Georg Cantor, translating German 'Menge.' The notation 2^S for a power set, still used today, is a quiet nod to that same 2^n relationship baked right into the symbol.