In this article, an event-triggered adaptive control strategy is presented for nonlinear pure-feedback multi-agent systems, and the problem of the unknown control gain is also considered. In contrast to most of the existing results, each agent's control item is a power exponential function, and this problem is handled by utilizing the “adding a power integrator" technique. Based on the Nussbaum gain technique, a control scheme is presented to handle the problem concerning unknown control gains. The tracking differentiator is used to eliminate the problem of “explosion of complexity” in the backstepping method. Furthermore, an event-triggered control strategy is designed to reduce the communication burden and the computational cost. It is proved via the Lyapunov stability method that the consensus tracking errors can converge to a small neighborhood of the origin and all signals of the closed-loop systems are semi-globally uniformly ultimately bounded. Finally, some simulation results are proposed to verify the effectiveness of the theoretical results.