This one is Easy!

Now, for any value of $z>0$

We get $0^z = 0$

You can try it with a few values of $z$

$z = 1\implies 0^z = 0^1 = 0\\z = 2\implies 0^z = 0^2 = 0 \times 0 = 0\\z = 3\implies 0^z = 0^3 = 0 \times 0 \times 0 = 0$

On the other hand, for any value of $z<0$ , the expression $0^z$ is undefined, because

$z < 0 \implies 0^z = \dfrac{1}{0^{-z}} = \dfrac{1}{0} = \text{Undefined}$

$z = 0$ is a special case

Mathematicians claim that $0^0=1$

Read more about the value of $0^0$ in this article