We present preliminary results from a systematic spectral study of pulsars and their wind nebulae using the Chandra X-Ray Observatory . The superb spatial resolution of Chandra allows us to differentiate the compact object ’ s spectrum from that of its surrounding nebulae . Specifically , for six Crab-like pulsars , we compare spectral fits of the averaged pulsar wind nebulae ( PWN ) emission to that of the central core using an absorbed power-law model . These results suggest an empirical relationship between the bulk averaged photon indicies for the PWNe and the pulsar cores ; \Gamma _ { PWN } = 0.8 \times \Gamma _ { Core } +0.8 . The photon indices of PWNe are found to fall in the range of 1.3 < \Gamma _ { PWN } < 2.3 . We propose that the morphological and spectral characteristics of the pulsars observed herein seem to indicate consistent emission mechanisms common to all young pulsars . We point out that the previous spectral results obtained for most X-ray pulsars are likely contaminated by PWN emission .