Power law rheology is of widespread occurrence in complex materials that are characterized by the presence of a very broad range of microstructural length and time scales. Although phenomenological models able to reproduce the observed rheological features exist, in general a well-established connection with the microscopic origin of this mechanical behavior is still missing. As a model system, this work focuses on a fractal colloidal gel. We thoroughly characterize the linear power law rheology of the sample and its age dependence. We show that at all sample ages and for a variety of rheological tests, the gel linear viscoelasticity is very accurately described by a fractional Maxwell (FM) model, characterized by a power law behavior. Thanks to a unique setup that couples small-angle static and dynamic light scattering to rheological measurements, we show that in the linear regime, shear induces reversible nonaffine rearrangements which might be at the origin of the power law rheology and we discuss the possible relationship between the FM model and the microscopic structure of the gel. (C) 2018 The Society of Rheology.