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Uh.... I think your units are off to say the least.

I'm assuming e is the electron charge. The constants hbar, c and G don't have units of charge to cancel that out.

Yes, e stands for the electron charge. However, hbar times c divided by e squared is the fine structure constant to the minus 1. (hbar * c/e^2)= approx. 137 (hbar * c/e^2)raised to the third power equals: 2.57338006 E6 [(hbar * c/e^2)]^3 * [(hbar * c/G^3)]^3 = (pi^3 * 10^20) moving (pi^3 * 10^20) to the left denominator and G^9 to the right numerator, we have: [(hbar * c/e^2)]^3 times [(hbar * c * pi-1)^3]/10^20] = G^9 [2.57338006 E+6] X [1.019159191E-71] = 2.6226839407 E-65 taking 2.6226839407E-65 to the ninth root we get: 6.6727538776 E-8 in cgs unitsBecause (hbar * c/e^2) is dimensionless and,because (hbar * c/G^3) is dimensionless,this equation works just as well when done in SI units.6.6727538776 E-8 in cgs units and 6.6727538776 E-11 in SI units agrees very closely with NIST figures.