  The coronal activity-rotation relationship is considered to be a proxy for
the underlying stellar dynamo responsible for magnetic activity in solar and
late-type stars. While this has been studied in considerable detail for
partly-convective stars that are believed to operate an interface dynamo, it is
poorly unconstrained in fully-convective stars that lack the necessary shear
layer between radiative core and the convective envelope. We present new X-ray
observations of 19 slowly-rotating fully-convective stars with rotation periods
from the MEarth Project. We use these to calculate X-ray luminosities (or upper
limits for undetected sources) and combine these with existing measurements
from \citet{wrig16b}. We confirm the existence of fully-convective stars in the
X-ray unsaturated regime and find that these objects follow the same
rotation-activity relationship seen for partly-convective stars. We measure the
power-law slope of the relationship between Rossby number (the ratio of the
rotation period to the convective turnover time) and the fractional X-ray
luminosity for X-ray unsaturated fully-convective stars for the first time, and
find it to be consistent with that found for partly-convective stars. We
discuss this implications of this result for our understanding of stellar
magnetic dynamos in fully- and partly-convective stars. Finally, we also use
this data to improve empirical estimates of the convective turnover time for
fully-convective stars.
