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Abstract This paper is devoted to the global stabilization and practical tracking for a class of uncertain nonlinear systems. The presence of unknown powers and serious parameter unknowns makes the systems in question essentially different from those in the related works. By skillfully combining adaptive technique and adding a power integrator, two novel adaptive state-feedback controllers are successfully designed to achieve global stabilization and practical tracking, respectively. Remarkably, the typical feature of the two controllers lies in the introduction of the adaptive dynamic and the terms of lower and higher powers (with respect to the unknown system powers), which makes the controller powerful enough to compensate the serious parameter unknowns and the unknown powers of the system. Finally, simulation examples are provided to illustrate the effectiveness of the designed controllers. [ABSTRACT FROM AUTHOR]