<p>The existence of higher-order interactions represents a significant frontier issue in the study of complex system dynamics, profoundly influencing collective behavior properties. According to the traditional Kuramoto model, this paper establishes a higher-order Kuramoto model incorporating first-, second-, and third-order couplings within a simplex complex network framework. The model adopts a power format based on node degree characterizing the first-order coupling strength and replaces the traditional constant setting. Then, we derive the necessary synchronization stability condition of coupled oscillatory model via the Master Stability Function (MSF) method. Furthermore, the impact of higher-order interactions and power exponents on the synchronous stability of systems is investigated. Our results indicate that the variations in third-order coupling strength and the exponents significantly influence system synchronizability. In specific, larger values of the third-order coupling strength shrink the synchronous range and play the negative role on the synchronizability under fixed exponent values. In addition, the smaller exponent values expand the synchronized region, whereas larger exponents shrink the synchronized range. These results imply that one can select the appropriate values of parameters to enhance the synchronizability of the coupled systems.</p>