We prove that for any odd integer N and any integer 0$"> n > 0 , the N th power of a product of n commutators in a nonabelian free group of countable infinite rank can be expressed as a product of squares of 2 n + 1 elements and, for all such odd N and integers n , there are commutators for which the number 2 n + 1 of squares is the minimum number such that the N th power of its product can be written as a product of squares. This generalizes a recent result of Akhavan-Malayeri.