  Recently, it was shown that the power-Maxwell (PM) theory could remove the
singularity of the electric field \cite{PM2}. Motivated by a great interest in
three-dimensional black holes and a surge of success in studying massive
gravity from both the cosmological and astrophysical points of view, we
investigate three-dimensional black hole solutions in de Rham, Gabadadze, and
Tolley (dRGT) massive theory of gravity in the presence of PM electrodynamics.
First, we extract exact three-dimensional solutions in this theory of gravity.
Then we study the geometrical properties of these solutions. Calculating
conserved and thermodynamic quantities, we check the validity of the first law
of thermodynamics for these black holes. We also examine the stability of these
black holes in the context of the canonical ensemble. We continue calculating
this kind of black hole's optical features, such as the photon orbit radius,
the energy emission rate, and the deflection angle. Considering these optical
quantities, finally, we analyze the effective role of the parameters of models
on them.
