So, what it is; I'm hoping for help from a mathematician, should one happen to read this. But first, a complaint, the discussion of which may well end up taking longer than the actual topic…

The commonly given definition of a mathematical exponent (rather than an exponent of mathematics, which would be an enthusiastic maths teacher; I'm here all week, folks!) is that it represents how many times a given number should be multiplied by itself. Even as a child—a rather pedantic child, I should admit, but I know for a fact that I wasn't the only one—when I was given this explanation by a maths teacher, I found it both misleading and ambiguous.