This paper studies the Kadomtsev-Petviashvili-Burgers equation with power law nonlinearity that arises in the study of dusty plasmas. The traveling wave hypothesis reveals the topological 1-soliton solution or the shock wave solution to the equation. Painleve analysis is performed to check the Painleve property and the Lie-group formalism is applied to investigate the symmetries. We derive the infinitesimals that admit the classical symmetry group. Partial differential equations are investigated by solving the corresponding characteristic equations. The Lie group formalism is again applied on investigated partial differential equations to deduce symmetries and the ordinary differential equations deduced from subalgebras are further studied and some exact solutions are obtained.