  In this paper we prove that if $\kappa$ is a singular cardinal with
uncountable cofinality, then every power of a given topological space with
precaliber $\kappa$ has precaliber $\kappa$ as well. Furthermore, if
$\{X_\alpha : \alpha<\lambda\}$ is a family of topological spaces with
precaliber $\kappa$ and $\lambda<cf(\kappa)$, then $\kappa$ is a precaliber for
the topological product $\prod\{X_\alpha : \alpha<\lambda\}$.
