Solution:
Permeability of free space
$$
\begin{aligned}
&\mu_{0}=\frac{2 \pi \times \text { force } \times \text { distance }}{\text { current } \times \text { current } \times \text { length }} \\
&\text { Dimensional formula of } \mu_{0}=\frac{\left[M L T^{-2}\right][L]}{[A][A][L]} \\
&=\left[M L T^{-2} A^{-2}\right]
\end{aligned}
$$