Building on work of Terada, we prove that h-homogeneity is productive in the
class of zero-dimensional spaces. Then, by generalizing a result of Motorov, we
show that for every zero-dimensional space $X$ there exists a zero-dimensional
space $Y$ such that $X\times Y$ is h-homogeneous. Also, we simultaneously
generalize results of Motorov and Terada by showing that if $X$ is a
zero-dimensional space such that the isolated points are dense then $X^\kappa$
is h-homogeneous for every infinite cardinal $\kappa$. Finally, we show that a
question of Terada (whether $X^\omega$ is h-homogeneous for every
zero-dimensional first-countable $X$) is equivalent to a question of Motorov
(whether such an infinite power is always divisible by 2) and give some partial
answers.