  An exact analysis of the N-dimensional blackbody radiation process in a
nonextensive \`a la Tsallis scenario is performed for values of the
nonextensive's index in the range ($0<q<1$). The recently advanced ``Optimal
Lagrange Multipliers" (OLM) 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 are investigated.
  PACS: 05.30.-d, 95.35.+d, 05.70.Ce, 75.10.-b Keywords: Tsallis
Thermostatistics, Blackbody radiation.
