<p>This study investigates the nonlinear flow behavior of Powell-Eyring fluids over an exponentially stretching sheet, incorporating the effects of radiative heat transfer. The Powell-Eyring fluid model, which captures both shear-thinning and shear-thickening characteristics, leads to highly nonlinear and coupled boundary layer equations that are generally intractable by traditional analytical techniques. To overcome these challenges, the governing partial differential equations are reduced to ordinary differential equations using similarity transformations and subsequently solved using the Hermite wavelet method, a powerful numerical tool well-suited for semi-infinite domains. The Hermite wavelet method offers localized basis functions with orthogonality and rapid convergence, eliminating the need for domain truncation and effectively resolving steep gradients. The influence of key parameters such as stretching rate, fluid viscosity, and non-Newtonian parameters is analyzed in detail. Results reveal that increasing the stretching rate intensifies the fluid velocity near the sheet while thinning the boundary layer. The accuracy and robustness of the method are validated through comparisons with existing analytical and semi-analytical solutions, demonstrating excellent agreement. Moreover, the computational efficiency and precision of the Hermite wavelet approach underscore its potential for tackling a wide range of nonlinear fluid flow problems in engineering and industrial applications.</p>