> x^y should be zero if you approach (0,0) along the x=0 axis, and it should be one if you approach along the y=0 axis. Technically, 0^y is 0 only if you appr

> x^y should be zero if you approach (0,0) along the x=0 axis, and it should be one if you approach along the y=0 axis. Technically, 0^y is 0 only if you approach it from the right: y>0. To the left of 0 it is indeterminate or infinity depending on how you look at it. x^0, however, makes sense for all x and is always 1