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The local to global property for an equation ψ over a group G asks to show that ψ 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 ψ. In particular we use it to show that the local to global property holds for m-powers in free groups.arXiv:1907.05968v2 fatcat:lwbrqsgfdjdzxjdfku3xjhnm6m