The interpretation of long wavelength geoid and plate motions on the basis of dynamic Earth models has usually been done assuming linear viscous rheologies in the mantle. In this paper, we develop spherical three-dimensional models of mantle circulation using power-law creep rheologies with an exponent n=3. In the steady state limit, the stress-dependent rheologies only modify the amplitude of the topography supported by an internal load by a few percents with respect to the linear predictions. The geoid anomalies induced by internal loads can be affected by around 20%. These changes are also occurring at degrees and orders different from those of the mass anomaly itself. As the geoid spectrum is strongly decreasing with degree, the dynamic topography induced at high degrees can be contaminated in a non-negligible way by the low degree loads. The main contamination occurs at a harmonic triple of that of the most important load. The flow structure is much more dependent on the form of the constitutive law than the dynamic topography and the geoid. On the contrary to linear rheology, a power-law creep is able to sustain a toroidal velocity field. However, this toroidal component only carries a few percents of the kinetic energy and thus, the non linear creep with n=3 cannot by itself explain the observed quasi-equipartition of plate tectonic energy between toroidal and poloidal components.