F ∝ \(\frac{M_1 M_2}{r^2}\)

F = \(\frac{GM_1M_2}{r^2}\) 

where F is the force of attraction
M\(_1\) and M\(_2\) are the masses of the two bodies, r is the distance between them, and G is the universal gravitational constant

Therefore, G = \(\frac{Fr^2}{M_1M_2}\)

Dimension for F = \(\frac{\text{ML}}{T.T}\) = MLT\(^{-2}\)
The dimension for G = \(\frac{MLT^{-2}L^2}{M.M}\) = \(\frac{L^3T^{-2}}{M}\)

= M\(^{-1}\)L\(^3\)T\(^{-2}\)
In comparison with M\(^x\)L\(^y\)T\(^z\), the values for x, y and z = -1, 3, -2