Let $\mathcal{C}$ be a cartesian closed category. I'm working on a problem that asks me to show that for $X,Y,Z\in\text{ob}(\mathcal{C})$ there is a natural isomorphism $(Y^Z)^X\cong Y^{Z\times X}$. It's easy enough to show the two are isomorphic as objects of $\mathcal{C}$ by showing one satisfies the universal property of the other, but I not sure what is the correct perspective to show neutrality. Do we want to show isomorphism of functors $(Y^{-})^{-},Y^{-\times -}\colon \mathcal{C}^\text{op}\times \mathcal{C}^\text{op}\to \mathcal{C}$? Or is it an isomorphism between $(-^-)^X$ and $(-)^{-\times X}$?
I know one can prove this using the fact that the $(-)^X$ is right adjoint to $-\times X$, but I am interested in explicitly constructing the isomorphism.