From the point of view of two distinct methods, we will construct new multiple types of private exact solutions of the (2+1)-dimensional modied Zakharov{Kuznetsov equation (MZKE) which is a famous model in plasma physics. The suggested methods for this pur- pose are the extended simple equation method (ESEM) and the Paul{Painleve approach method (PPAM). Moreover, the numerical solutions corresponding to the achieved so- lutions are demonstrated in the framework of the variational iteration method (VIM). Furthermore, we will demonstrate a good comparison not only between our achieved solutions but also with that realized previously by other authors who studied this model before.