An exact analysis of the N-dimensional blackbody radiation process in a nonextensive à la Tsallis scenario is performed for values of the nonextensive's index in the range (0< q<1). The recently advanced “Optimal Lagrange Multipliers” technique has been employed. The results are consistent with those of the extensive, q=1 case. The generalization of the celebrated laws of Planck, Stefan-Boltzmann and Wien is investigated.