Density of power-free values of polynomials II

In this paper we prove that polynomials F(x1,⋯,xn)∈Z[x1,⋯,xn] of degree d≥3, satisfying certain hypotheses, take on the expected density of (d−1)-free values. This extends the authors' earlier result in [14] where a different method implied the similar statement for polynomials of degree d≥5.