The dimensions [MLT A - 2 ^ - 2 ] belong to the

Force, $F = \dfrac{{q}_{1}{q}_{2}}{4\pi{ε}_{0}{r}^{2}}$ or ${ε}_{0} = \dfrac{{q}_{1}{q}_{2}}{4\pi{r}^{2}F}$

Charge = current $\times$ time

Force = mass $\times$ acceleration

Thus, dimensional formula of electric permittivity,

\left[{ε}_{0}\right] = \dfrac{\left(IT\right)\left(IT\right)}{\left({L}^{2}\right)\left({MLT}^{- 2}\right)}= {M}^{- 1}{L}^{- 3}{T}^{4}{I}^{2}$</p><p>Since speed of light,$c = \dfrac{1}{\sqrt{{ε}_{0}{\mu}_{0}}}$</p><p>Therefore, dimensional formula of magnetic permeability, \left[{\mu}_{0}\right] = \dfrac{1}{\left[{c}^{2}{ε}_{0}\right]} = \dfrac{1}{\left({L}^{2}{T}^{- 2}\right)\left({M}^{- 1}{L}^{- 3}{T}^{4}{I}^{2}\right)}$

$⇒ \left[{\mu}_{0}\right] = {MLT}^{- 2}{I}^{- 2}$