In this paper, the problem of adaptive neural backstepping control is investigated for uncertain high-power stochastic nonlinear systems with prescribed performance under arbitrary switchings. For the control of high-power nonlinear systems, it is assumed that unknown system dynamics and arbitrary switching signals are unknown. Firstly, by utilizing the prescribed performance control (PPC), the prescribed tracking control performance is ensured. Then, RBF neural networks are employed to deal with completely unknown system dynamics, and only one adaptive parameter is constructed to overcome the over-parameterization. Finally, based on the common Lyapunov stability method, the adaptive neural control method is proposed, which decreases the number of learning parameters. It is shown that the designed common controller can ensure that all the closed-loop signals are semi-globally uniformly ultimately bounded (SGUUB), and the prescribed tracking control performance is guaranteed under arbitrary switchings. The simulation results show the effectiveness of the proposed scheme.