Question 8
Let $Q_{\gt 0}$ denote the set of all positive rational numbers. Find all functions $f: Q_{\gt 0} \to Q_{\gt 0}$ satisfying
$$
f(x^2 f(y)^2) = f(x)^2 f(y), \text{ for all } x, y \in Q_{\gt 0}.
$$
$$
f(x^2 f(y)^2) = f(x)^2 f(y), \text{ for all } x, y \in Q_{\gt 0}.
$$