Powers of commutators as products of squares (Q700911)

Let \(F\) be a non-Abelian free group and \(x,y\) be two distinct elements of a free generating set. It is proved that \([x,y]^n\neq a^2b^2\), for any odd integer \(n>0\) and any two elements \(a,b\in F\), and there exist three elements \(v\), \(w\) and \(z\) in \(F\) such that \([x,y]^n=u^2v^2w^2\). However it is mentioned that there are commutators in \(F\) which can be expressed as a product of squares of two elements in \(F\).