In this paper, a generalized (1+2)-dimensional Jaulent-Miodek equation with a power law nonlinearity is examined, which arises in numerous problems in nonlinear science. The computed conservation laws reside in enormously crucial areas both at the foundations of nonlinear science such as biology, physics and other related areas. Exact solutions are acquired using the Lie symmetry method. In addition to exact solutions, we also present conservation laws. The arbitrary functions in the multipliers lead to infinitely many conservation laws.