Using keen physical insight developed from years of experience, taylor decided the radius r of the fireball should depend only on time since the explosion, t, the density of the air, ρ, and the energy of the initial explosion, e. thus, he made the educated guess that r = keaρbtc for some dimensionless constant k and some unknown exponents a, b, and c. given that [e] = ml2t−2, determine the values of the exponents necessary to make this equation dimensionally consistent. (hint: notice the equation implies that k = re−aρ−bt−c and that [k] = 1.)