In this paper we consider heterogeneous diffusion processes with the power-law dependence of the diffusion coefficient on the position and investigate the influence of external forces on the resulting anomalous diffusion. We obtain analytic expressions for the transition probability as well as for the first and the second moments. By using these expression we demonstrate that the power-law exponent in the dependence of the mean square displacement on time does not depend on the external force. When the external force has a power-law exponent different than the power-law exponent of the noise induced drift, we can observe anomalous diffusion only in limited time interval. We expect that the results obtained in this paper may be useful for a more detailed understanding of anomalous diffusion processes in heterogeneous media.