How can I plot $y^x$? To keep things simple and to not have another $z$ variable on the other end of the equation, let's assume $y^x=10$. As long as that value is not $0$, the curve we get should look about the same.
The problem arises when $x$ is negative. The thing is, when $x$ is an odd, then y can only be a positive number. However, when $x$ is even, y can be either positive or negative. Therefore, if you look at the $x$ negative side of the graph, you would be able to mark a point whenever $x$ is even, but there would be no point when it is odd. So how could you graph such a thing? I simply have no idea what happens between two negative odd numbers (e.g. how does the curve behave between $-1$ and $-3$?)
As always, I tried WolframAlpha, and even it has trouble graphing the thing! Here is what it ends up with.