Using mass (M), length (L), time (T), and electric current (A) as fundamental quantities, the dimensions of permittivity will be
MLT−1A−1
MLT−2A−2
M−1L−3T4A2
M2L−2T−2A
By Coulomb's laws, F=14πε0×q1q2r2
ε0=q1q24π×F×r2
Taking dimensions, ε0=(AT)(AT)ML1T−2×L2=M−1L−3T4A2