Interesting. When I took high school math as a kid, there weren't many explanations, (and for some reason, I wasn't up for looking them up/figuring them out myself- weird, 'cause I totally was up for that sort of thing in some other classes) - just x^(a+b) = x^a * x^b and x^0=1 -- memorize these facts, with the emphasis on memorization rather than on the connection between those facts. Most of what I remember is a lot of guess and check and factorization; something I automated using the rom basic on my Tandy model 100. These were the mid '90s, and looking back with a less resistant mind, I think they really were trying to get us to develop a mathematical intuition, and that if I had read the math text book the way I read the history or English lit textbooks (they were full of stories!) I would have done just fine. But I
still can't read math books the way I read literature, and I haven't figured out why yet. I know my first decade of reading, I skipped a lot, like if I didn't understand something, I moved on and filled out the blanks from what I did understand as best I could. (These days when I'm reading literature I get all excited when I see a word or phrase I don't understand, and I immediately stop and research. (the world is awesome for that today. Once I was blocked on my way home, waiting for a family of skunks to move off of the trail. I was introduced to rimbaud by miller, so I bought and downloaded a bunch of his stuff to my kindle. By the time I was done reading, it was dark and the skunks started to approach me, so I took off (without incident) but I wish I could do that with math, and I'm not quite sure why I cant. I mean, reading things I half understand, and halfway getting something out of it.)
the calculus explanation I heard from a friend that I was talking about this about was extrapolating from x^.5 x^.4, etc, etc, and as the exponent approaches 0 the answer approaches 1 for all non zero values of x - but this was maybe two years back and the friend in question was educated overseas, and I still am not educated enough to use calculus notation to write that down (or even really to understand if I understood him correctly.) so it could be garbled, or only tradition on the continent, or something like that.