This looks to me like actual correct usage of the term exponential. Surprisingly correct usage of that term is rare, even in technical writing. Let's say each

This looks to me like actual correct usage of the term exponential. Surprisingly correct usage of that term is rare, even in technical writing. Let's say each dimensions added has a finite set of N possible values. Then for k dimensions there are a total N^k possibilities. Combinatorical growth would actually be faster still, scaling like k!.