On the infinite powers of large zero-dimensional metrizable spaces

We show that X^λ is strongly homogeneous whenever X is a non-separable zero-dimensional metrizable space and $λ$ is an infinite cardinal. This partially answers a question of Terada, and improves a previous result of the author. Along the way, we show that every non-compact weight-homogeneous metrizable space with a $π$-base consisting of clopen sets can be partitioned into $κ$ many clopen sets, where $κ$ is the weight of X. This improves a result of van Engelen.