$\rho=h^{} m_{e}^{b} c^{c} e^{d} \varepsilon_{0}^{f}$

where, $k=$ a numeric constant.

Now, substituting dimensions of different physical constants, we have

$\left[ ML ^{3} T ^{-3} A ^{-2}\right]=k\left[[ \mathrm { ML } ^ { 2 } \mathrm { T } ^ { - 1 } ] ^ { k } \left[ M ^{b}\left[ LT ^{-1}\right]^{c}\right.\right.$

$\left.[ AT ]^{d}\left[ M ^{-1} L ^{-3} T ^{4} A ^{2}\right]^{f}\right]$

Equating dimensions, we have

$1=a+b-f$

$3=2 a+c-3 f$

$-3=-a-c+d+4 f$

$-2=d+2 f$

Solving these, we get

$a=2$

$b=-1$

$c=-1$

$d=-2$

$f=0$

So, resistivity can be expressed as

$\rho=k\left(\frac{h^{2}}{m_{e} c e^{2}}\right)$