ISL 2018 A1

Let $\mathbb{Q}_{>0}$ denote the set of all positive rational numbers. Determine all functions $f: \mathbb{Q}_{>0} \rightarrow \mathbb{Q}_{>0}$ satisfying for all $x, y \in \mathbb{Q}_{>0}$. $$f\left(x^{2} f(y)^{2}\right)=f(x)^{2} f(y)$$ (Switzerland)