This article studies the adaptive state feedback stabilization problem of stochastic nonlinear systems with many uncertainties, such as parametric uncertainties, time-varying delay, unknown powers, and stochastic inverse dynamics. By virtue of the adding-a-power-integrator technique, an adaptive control scheme together with a novel state feedback control law is proposed to deal with these unknowns. Compared with the existing literature, both of adaptive dynamics, higher and lower powers are introduced into the construction of our controller. Based on some ideas of Lyapunov function, we analyze the global stabilization of the whole system. Finally, a simulation example is given to show the effectiveness of our theoretical results.