The expression $\frac{1}{\mu_0 \epsilon_0}$ is related to the speed of light $ c $, given by the equation:

$ c = \frac{1}{\sqrt{\mu_0 \epsilon_0}} $

Therefore, we have:

$ \frac{1}{\mu_0 \epsilon_0} = c^2 $

The speed of light $ c $ has the dimensions of $\text{L T}^{-1}$, where $\text{L}$ is the dimension of length and $\text{T}$ is the dimension of time. Thus, when squared, the dimensions become:

$ c^2 = (\text{L T}^{-1})^2 = \text{L}^2 \text{T}^{-2} $

Hence, the dimensions of $\frac{1}{\mu_0 \epsilon_0}$ are $\text{L}^2 \text{T}^{-2}$.