The dimension of $(\mu _{ 0 }\epsilon _{ 0 })^{-1/2}$ are:

We have to find dimensions of $\left(\mu_{0} \varepsilon_{0}\right)^{-1 / 2}$

Where $\mu_{0}$ denotes permeability and $\varepsilon_{0}$ denotes permitivity

$\begin{array}{l} \left(\mu_{0} \varepsilon_{0}\right)^{-1 / 2}=\text { speed of light } \quad\left(\because\left(\mu_{0} \varepsilon_{0}\right)^{-1 / 2}=c\right) \\ \frac{1}{\left(\mu_{0} \varepsilon_{0}\right)^{1 / 2}}=\frac{L}{T} \Rightarrow \frac{1}{\left(\mu_{0} \varepsilon_{0}\right)^{1 / 2}}=\left[L T^{-1}\right] \\ \Rightarrow \text { Dimension of }\left(\mu_{0} \varepsilon_{0}\right)^{-1 / 2}=\left[L T^{-1}\right] \end{array}$