We had the statement that with an exact sequence of multiplicatively written abelian groups $U \mapsto V \mapsto W \mapsto X \mapsto Y$ and in $U$, $V$, $X$, $Y$ every group element has a unique $n$-th root ($n \in \mathbb{Z}$) That $W$ has this property as well.
How do I see that? Does it help me that the $n$ roots form a group under multiplication? Or why is that? Any help/hint/tipp would be great :)