  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
(Gamma) for the PWNe and the pulsar cores; Gamma_PWN = 0.8 X 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.
