Planck's constant (h), speed of light in vacuum (c) and Newton's gravitational constant (G) are three fundamental constants. Which of the following combinations of these has the dimensions length?

In forms of h, c and G, length can be expressed as                     L = (h)a (c)b (G)eWriting dimensions on both sides, we get                    [M0 LT0] = [ ML2T-1]a [LT-1]b[M-1 L3T-2] c                                  = Ma-cL2a+b+3c T-a-b-2cOn comparing powers of M, Land T on both sides, we get                         a - c = 0, 2a + b + 3 c = 1and            - a - b - 2c = 0On solving, we get                       a∣=c=12 and b=−32∴  Dimensions of length, L=(h)1/2(c)−3/2(G)1/2=hGc3/2