Density of power-free values of polynomials II

In this paper we prove that polynomials $F(x_1, \cdots, x_n) \in $\mathbb{Z}$[x_1, \cdots, x_n]$ofdegree$d \geq 3$, satisfying certain hypotheses, take on the expected density of $(d-1)$-free values. This extends the authors’ earlier result where a different method implied the similar statement for polynomials of degree $d\ge 5$.