  The local to global property for an equation $\psi$ over a group G asks to
show that $\psi$ is solvable in G if and only if it is solvable in every finite
quotient of G. In this paper we focus that in order to prove this local to
global property for free groups $G=F_k$, it is enough to prove for k less or
equal the number of parameters in $\psi$. In particular we use it to show that
the local to global property holds for m-powers in free groups.
