  In recent years, analyzing the bimodality in the size distribution of small
planets, i.e., the `radius valley', has given us unprecedented insight into the
planet formation process. Here we explore the properties of the radius valley
for low mass stars, assuming that the core-powered mass-loss is the dominant
process shaping the small exoplanet population. We show that the slope of
radius valley in the planet size-orbital period space, to first-order, does not
vary with stellar mass and has a negative slope of $\text{d log}R_p/\text{d
log}P \simeq -0.11$ even for stars as small as 0.1 $M_\odot$, as observed in
latest studies. Furthermore, we find that the slope of the radius valley in the
planet size-stellar mass space is $\text{d log}R_p/\text{d log}M_\ast \simeq (3
\zeta - 2)/36$ where $\zeta$ is given by the stellar mass-luminosity relation
$L_\ast \propto M_\ast^\zeta$. Because $\zeta$ is $\gtrsim$ 2 and increases
with stellar mass, we predict that the radius valley has a positive slope in
the planet size-stellar mass space across FGKM dwarfs. This slope, however,
decreases (increases) in magnitude towards lower (higher) mass stars, due to
the variation of $\zeta$ with stellar mass. While around 1.0 $M_\odot$ stars
the slope is $\text{d log}R_p/\text{d log}M_\ast \sim 0.37$, it is as low as
$\sim 0.13$ around 0.1 $M_\odot$ stars. In addition, we find that the radius
valley is narrower and less empty around lower mass stars. Finally, we show
that predictions for the radius valley for core-powered mass-loss and
photoevaporation become increasingly distinct for lower mass stars.
