In this work, we extend the resummation of multiple medium-induced emissions to apply to dynamically expanding media. This is done by recasting the quenching weight as the solution of a rate equation with medium-induced partonic splitting functions that are sensitive to the expansion. We perform the calculations in the framework of Baier-Dokshitzer-Mueller-Peigne-Schiff-Zakharov (BDMPSZ) formalism for multiple soft scatterings with a time-dependent transport coefficient. Furthermore, we discuss the validity of a dynamical scaling law that relates the spectrum in an expanding medium to the equivalent static case with re-scaled medium parameters and test the scaling law for the gluon splitting rates.