I’ve always wondered why anything to the zero power is 1 instead of 0. This is the first time I’ve seen a proof for it. Thank you for that.
As for 0 to the 0th power, your conclusion that 2 = x * 0 is indeterminate could be taken further to show that 2 = 0 (since any real number, x times zero is zero) and therefore 2/0 must be equivalent to 0/0, which is obviously 0. Or is it obviously 1?
You lost me on the derivatives. I hope you have plans for future columns on elementary calculus.