A novel application of intelligent computing is presented to study the dynamics of the power-law fluidic problem (PLFP) of moving-wedge and flat-plate models using a multilayer structure of feedforward neural networks (FFNNs) optimized with the Levenberg-Marquardt method (LMM), i.e. FFNN-LMM. The reference dataset for inputs and targets of FFNNs is generated through the Adams numerical solver for the non-Newtonian power-law fluidic system in the case of dilatant, pseudo-plastic, and other thinning/thickening fluids with different values of wedge angle and velocity ratio parameters. The designed FFNNs backpropagated with LMM are constructed with the help of arbitrary samples for training, testing, and validation via mean squared error (MSE)-based figure of merit. Comparison of the proposed computing platform FFNN-LMM with reference standard solutions in terms of MSE, state transition statistics of the algorithm, error histogram studies, and regression outcomes endorse the accuracy and convergence for solving different scenarios in PLFPs.