What steep mathematical relationship approximates Luminosity (L) to Mass (M) for most main sequence stars?

$ ext{L} oldsymbol{\propto} ext{M}^{3.5}$.

For main sequence stars falling roughly within the mass range of $0.1$ to $50$ times the Sun's mass ($ ext{M}_{ ext{odot}}$), there exists a very steep correlation between how massive a star is and how brightly it shines. This relationship is commonly approximated using the mass-luminosity relation: Luminosity is proportional to Mass raised to the power of 3.5 ($ ext{L} oldsymbol{\propto} ext{M}^{3.5}$). The high exponent in this approximation demonstrates that even small increases in mass lead to dramatically large increases in energy output. For instance, a star five times the Sun's mass produces luminosity nearly 280 times greater than the Sun, whereas a star only one-tenth the Sun's mass is exceedingly faint, producing only about 1/3160th of the Sun's light. This steep dependence explains why lower-mass stars, which are far more numerous, dominate the population of stars found along the main sequence band.