This work addresses the event-triggered finite-time control problem for a class of uncertain switched nonlinear systems with arbitrary switchings, whose powers are positive odd rational numbers. The key difference from the results of similar problems is that the systems considered in this article are more general, which contains a special case when the powers are equal to 1, and the powers have switching signals. It is well known that such nonlinear systems have challenges because of the uncontrollability in the linearization process and the backstepping technique that successfully developed for low-order systems fail to work. To tackle this issue, combining the backstepping method, event-triggered strategy with adding one power integrator technique, an event-triggered control scheme is developed to make the controlled systems be globally finite-time stable. Besides, the Zeno-free behavior is proved to verify the feasibility of the proposed event-triggered mechanism. Finally, simulation results are given to validate the effectiveness of the developed control strategy.