We know that the speed of light in a vacuum, denoted by $c$, is given by the relation $c = \frac{1}{\sqrt{\mu_0\varepsilon_0}} = (\mu_0\varepsilon_0)^{-1/2}$. Since $(\mu_0\varepsilon_0)^{-1/2}$ represents speed (or velocity), its dimensions are the same as the dimensions of velocity, which is $[L T^{-1}]$.