<p>This paper is concerned with the design of event-triggered control strategy based on prescribed performance function for high-order nonlinear multi-agent systems with unknown time-varying powers. First, the powers of the multi-agent systems are considered to be unknown and time-varying functions, which is fundamentally different from many existing approaches. Then, an event-triggered mechanism based on a prescribed performance function is introduced under the single leader case, which guarantees that all outputs of follower agents track the output of leader, moreover, the tracking error converges into a predefined region within a specified settling time. In addition, radial basis function neural networks are applied to deal with the uncertain nonlinearities during the process of controller design. Furthermore, the proposed strategy is extended to address the containment tracking problem with multiple leaders, ensuring that all followers converge in the convex hull spanned by the leaders. Finally, the effectiveness of the proposed method is validated through simulation examples.</p>