A new method based on the polylogarithm function is used to derive an exact expression for the fractional emissive power of a blackbody in any arbitrary spectral band. Compared to all previously used methods the polylogarithm based method is unsurpassed in its simplicity. Displacement laws for the centroid of blackbody radiation in the linear wavelength and frequency spectral representations that make use of the polylogarithm based approach are also given.