$\rho=h^{} m_{e}^{b} c^{c} e^{d} \varepsilon_{0}^{f}$
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
$\rho=k\left(\frac{h^{2}}{m_{e} c e^{2}}\right)$
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