  Let $(M^N, g, e^{-f}dv)$ be a complete smooth metric measure space with
$\infty$-Bakry-\'Emery Ricci tensor bounded from below. We derive elliptic
gradient estimates for positive solutions of a weighted nonlinear parabolic
equation \begin{align*} \displaystyle \Big(\Delta_f - \frac{\partial}{\partial
t}\Big) u(x,t) +q(x,t)u^\alpha(x,t) = 0, \end{align*} where $(x,t) \in M^N
\times (-\infty, \infty)$ and $\alpha$ is an arbitrary constant. As
Applications we prove a Liouville-type theorem for positive ancient solutions
and Harnack-type inequalities for positive bounded solutions.
