= Solution
The <Yoneda embedding> preserves <categorical products>: for any $a$, maps $a\to c\times Y$ correspond naturally to pairs of maps $a\to c$ and $a\to Y$. Hence $H_{c\times Y}\cong H_c\times H_Y$. Using the <exponential in a presheaf category>, the <Yoneda lemma> and the exponential <universal property> in $\mathcal C$ gives
$$
\begin{aligned}
((H_Z)^{H_Y})(c)
&=\operatorname{Nat}(H_c\times H_Y,H_Z)\\
&\cong\operatorname{Nat}(H_{c\times Y},H_Z)\\
&\cong\mathcal C(c\times Y,Z)\\
&\cong\mathcal C(c,Z^Y)=H_{Z^Y}(c).
\end{aligned}
$$
Every <bijection> is natural in $c$, since it is given by precomposition or the natural exponential <adjunction>. Thus these component <bijections> are a <natural isomorphism> of <categorical presheaves>:
$$
\boxed{(H_Z)^{H_Y}\cong H_{Z^Y}.}
$$
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