Question 9
Let $\mathbb{Q}^{+}$ denote the set of all positive rational numbers. Determine all functions $f: \mathbb{Q}^{+} \rightarrow \mathbb{Q}^{+}$ with the property
$$
f\left(x^{2} f(y)^{2}\right) = f\left(x^{2}\right) f(y) \tag{*}
$$
for all $x, y \in \mathbb{Q}^{+}$.
$$
f\left(x^{2} f(y)^{2}\right) = f\left(x^{2}\right) f(y) \tag{*}
$$
for all $x, y \in \mathbb{Q}^{+}$.