Well, that is certainly interesting; a user who lays claim to being an educator who finds the idea that a language having rules is less than absolutely necessary. Since mathematics is nothing more than an elaborate form of communication, if your door equals my automobile, how in the world are we supposed to communicate correctly?
This is not something I "constructed" one day. This is an elementary truth that you apparently will do anything to refute or Heaven forbid you admit you're wrong. And I never said x^0 = 0 ... is that a typo?
And I noticed a subtle shift in your argument.
The question wasn't for something that could be used to explain real or negative exponents. The question originally posed concerned an easy conceptualization for x^0 and x^1, and I more than delivered. You can call it "mathematical trickery" all you want, and you can hold all the irrational beliefs about mathematics that you want as well. It doesn't change the fact that my explanation isn't hard to grasp, if the pupils in question have an understanding of basic axioms that we all learn in elementary school.
But I'll bite, anyway. "My" implicit 1 very much so applies to real and negative exponents. For real exponents, as the exponent approaches zero (i.e. gets smaller and smaller), the result approaches 1, and for negative exponents that get smaller and smaller, the result approaches 0. In all that, the central figure is always the ever-present 1 that exists beside all values. These assertions by themselves don't completely explain the concepts, I won't argue with that, but they nevertheless provide important conceptual starting points.
If I may give an opinion about this argument, I'd say it has not gone far since my posting of my "mini theorem," if it indeed has gone anywhere at all. I'd say it's ultimately up to the original poster of this thread to decide the "best" explanation. I should only need to make a true assertion once; several times is excessive. So, I'll not make more.