There is a bit of conflation going on here - the notation a^b being discussed is exponentiation of real numbers (or complex if you'd like to extend it that far). Of course, that notation is what inspired a^b being used to denote the number of maps from a set with cardinality b to a set with cardinality a (and the notation A^B to denote the set of all maps from B to A), but set theory was developed centuries after the likes of calculus and other important developments that touch on the reasoning used in the article linked in the OP.
