It’s one of those things that isn’t obvious from the definition, so we tend to define it in whatever way seems more sensible depending on what we’re working with.

A similar situation is 0/0. It’s indeterminate, so if you come across it as the y-value of a function, you don’t really know what the answer is. But based on the points around it, there’s probably a most sensible value it should be. For example, (5x^2)/x is 0/0 at x = 0, but it makes most sense to define it to be equal to 0 there, because that’s the limit when we approach it from either side. (This explanation isn’t exactly right, but I’m using it for the analogy.)

So, when it comes to 0^0, it usually makes sense to define it as being equal to 0. (Though I think I’ve heard it sometimes makes sense to define it as 1, too.)

Hope this helps.