What is the commonly approximated exponent (\alpha) for the mass-luminosity relation across most main-sequence stars?

Around 3.5

For the vast majority of stars residing on the main sequence, the exponent ($\\alpha$) used in the mass-luminosity relation ($L \propto M^\alpha$) is frequently approximated to be around $3.5$. This value reflects the overall physical conditions governing energy generation in typical hydrogen-fusing stars. While the text notes that this exponent is not universal—sometimes dropping closer to $2$ for lower-mass stars or climbing toward $4$ for the most massive stars—$3.5$ serves as the general benchmark for understanding the intense scaling of energy output relative to mass addition in these stellar engines.