This article investigates the asymptotic tracking control problem for full-state-constrained nonlinear systems with unknown time-varying powers. By introducing a nonlinear state-dependent transformation, a continuous bounded scalar function, and lower and higher powers into adding a power integrator control design, full-state constraints are skillfully handled without imposing frequently used feasibility conditions in traditional barrier Lyapunov function-based methods, and an asymptotic tracking control design is provided. It is proved that all the closed-loop signals are bounded, full-state constraints are not transgressed, and the asymptotic tracking is achieved.