An alternative but new nonlinear output regulation approach is proposed for a class of lower triangular nonlinear systems by using the tool of adding a power integrator. The invariant manifold is solved and represented in terms of various derivatives of disturbances and references. As such, it is unnecessary to suppose that the external disturbances being governed by certain exosystems anymore. The nonlinearities are not restricted to be sufficiently smooth due the the utilization of feedback domination approach. It is shown that the time taken to reach the desired invariant manifold from any initial states under external disturbances is guaranteed to be finite time. The control law is concise in structure for implementation since the feedback domination is implemented in each of the recursive design step.