If electronic charge $$e,$$ electron mass $$m,$$ speed of light in vacuum $$c$$ and Planck’s constant $$h$$ are taken as fundamental quantities, the permeability of vacuum $${\mu _0}$$ can be expressed in units of

Solution :
Let $${\mu _0}$$ related with $$e,m,c$$  and $$h$$ as follows.
$$\eqalign{ & {\mu _0} = k{e^a}{m^b}{c^c}{h^d} \cr & \left[ {ML{T^{ - 2}}{A^{ - 2}}} \right] = {\left[ {AT} \right]^a}{\left[ M \right]^b}{\left[ {L{T^{ - 1}}} \right]^c}{\left[ {M{L^2}{T^{ - 1}}} \right]^d} \cr & = \left[ {{M^{b + d}}{L^{c + 2d}}{T^{a - c - d}}{A^a}} \right] \cr} $$
On comparing both sides we get
$$\eqalign{ & a = - 2,b = 0,c = - 1,d = 1 \cr & \therefore \left[ {{\mu _0}} \right] = \left[ {\frac{h}{{c{e^2}}}} \right] \cr} $$