[pxx]

You've the proper definitions but are missing the context. An exponential with larger base still has an exponential multiplicative difference compared to an exponential with a smaller base.

We're comparing the growth rate of of two exponentials representing variable-length identifiers. We're not looking at a constant-length identifier (which is what you're doing with only looking at a^n). Notice the context of where exponential is used in the article: we are changing n from 5 to 8.