  In this paper, we consider Kropina change of $m$-th root Finsler metrics. We
find necessary and sufficient condition under which the Kropina change of an
$m$-th root Finsler metric be locally dually flat. Then we prove that the
Kropina change of an $m$-th root Finsler metric is locally projectively flat if
and only if it is locally Minkowskian.
