<p>This paper investigates the adaptive prescribed-time control for high-order nonlinear system with unknown time-varying powers. There is no doubt that the existence of the unknown powers makes the considered problem difficult and no prescribed-time control schemes have been obtained. Different from the existing asymptotic stability results, an adaptive prescribed-time control scheme is proposed with the aid of the backstepping method, where the terms of lower and higher powers are introduced to compensate the unknown input powers. It is ensured that all the signals are bounded and the system states can converge to zero in prescribed-time. A simulation example is given to illustrate the effectiveness of the proposed method.</p>