  The XMM-Newton Extended Survey of the TMC (XEST) is a large program designed
to systematically investigate the X-ray properties of young stellar/substellar
objects in the TMC. In particular, the area surveyed by 15 XMM-Newton pointings
(of which three are archival observations), supplemented with one archival
Chandra observation, allows us to study 17 BDs with M spectral types. Half of
this sample (9 out of 17 BDs) is detected; 7 BDs are detected here for the
first time in X-rays. We observed a flare from one BD. We confirm several
previous findings on BD X-ray activity: a log-log relation between X-ray and
bolometric luminosity for stars (with L*<10 Lsun) and BDs detected in X-rays; a
shallow log-log relation between X-ray fractional luminosity and mass; a
log-log relation between X-ray fractional luminosity and effective temperature;
a log-log relation between X-ray surface flux and effective temperature. We
find no significant log-log correlation between the X-ray fractional luminosity
and EW(Halpha). Accreting and nonaccreting BDs have a similar X-ray fractional
luminosity. The median X-ray fractional luminosity of nonaccreting BDs is about
4 times lower than the mean saturation value for rapidly rotating low-mass
field stars. Our TMC BDs have higher X-ray fractional luminosity than BDs in
the Chandra Orion Ultradeep Project. The X-ray fractional luminosity declines
from low-mass stars to M-type BDs, and as a sample, the BDs are less efficient
X-ray emitters than low-mass stars. We thus conclude that while the BD
atmospheres observed here are mostly warm enough to sustain coronal activity, a
trend is seen that may indicate its gradual decline due to the drop in
photospheric ionization degree (abridged).
