Suppose a quantity x can be dimensionally represented in terms of M, L and T, that is, [x] = Ma Lb Tc . The quantity mass
[X] = MaLbTc
[M] = [x.L-b.T-c]
now if a =0 then the solution (and the power) will be infinite. thus, then cannot be the exact dimension of the mass.
∴ a ≠ 0 can't be considered
thus, the mass can be represented in term of L, T and X only when a ≠ 0