Dimensions of $\frac{1}{{\mu }_0{ϵ}_0}$, where symbols have their usual meaning, are:

We know the velocity of light $c$ is given by:
$$c=\frac{1}{\sqrt{{\mu }_0{ϵ}_0}}$$
Squaring both sides:
$$c^2=\frac{1}{{\mu }_0{ϵ}_0}$$
Dimensions of velocity $c=[L{T}^{-1}]$.Dimensions of $c^2=[L{T}^{-1}{]}^2=[L^2{T}^{-2}]$.