The memory function for friction on a particle caused by a system of fixed or moving scatterers is evaluated for power law interaction. For a dilute system the study extends the steady-state calculation based on the Boltzmann equation to the case of frequency dependence due to the dynamics of the scattering process. For a dense gas an Enskog approximation can be used. The power law potential leads to scaling behavior of the dynamical friction coefficient as a function of reduced mass, coupling coefficient, and energy. (C) 2004 American Institute of Physics.