Yeah, I was just talking about the easier concept of x^0. Going the other way, 0^x it makes a lot less sense to me. I know that for all positive x, 0^x = 0. That it pops up to 1 at the origin means the thing is not smooth so drawing lines isn't going to help us.

Plotting z = y^x could be interesting but we're going to see asymptotic behaviour at x = y = 0 (when going in the x direction). So no easy wins there.