  We show that given a collection $X=\{f_1$, \ldots , $f_m\}$ of pure mapping
classes on a surface $S$, there is an explicit constant N, depending only on
$X$, such that their Nth powers $\{f_1^N$, \ldots , $f_m^N\}$ generate the
expected right-angled Artin subgroup of MCG($S$). Moreover, we show that these
subgroups are undistorted.
