= Solution
Write $x=m/M_\odot$ and absorb units into the <initial mass function> normalization, $dN=A x^{-3}dx$. The specified <mass-luminosity relation> is $L(x)=L_\odot x^3$, normalized to the Sun. Therefore the total stellar <mass> and <luminosity> are
$$
\frac{M_*}{M_\odot}=A\int_{0.1}^1x^{-2}dx=9A,
\qquad
\frac{L_*}{L_\odot}=A\int_{0.1}^1x^0dx=0.9A.
$$
The unknown normalization cancels. \b[The mass-to-light ratio is]
$$
\boxed{\Upsilon_* = 10\,\frac{M_\odot}{L_\odot}.}
$$
Low-mass <main sequence> stars dominate the stellar <mass>, while equal intervals of $x$ contribute equal <luminosity> under these particular exponents. More generally the <mass-to-light ratio of a power-law stellar population> with these exponents on $a<x<b$ is $(M_\odot/L_\odot)/(ab)$.
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