  We use a simple form of the K-essence theory and apply it to the classic
isotropic cosmological model and seek exact solutions. The particular form of
the kinetic term that we choose is $K \left(\phi, X \right)= K_0(\phi)X^m
+K_1$. The resulting field equations in the homogeneous and isotropic cosmology
(FRW)is considered. Several exact solutions are obtained.
