  We apply cosmological reconstruction methods to the $f(R,T)$ modified
gravity, in its recently developed scalar-tensor representation. We do this
analysis assuming a perfect fluid in a Friedmann-Lema\^{i}tre-Robsertson-Walker
(FLRW) universe. In this contribution we show the equations of motion obtained
and we present the solutions found for one of the particular cases we analysed:
an exponential evolution of the cosmological scale factor.
