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(C) Let $\mu_0$ be related to $e, m, c,$ and $h$ as follows: $\mu_0 = k e^a m^b c^c h^d$.The dimensional formula for $\mu_0$ is $[M L T^{-2} A^{-2}]$.

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$\left( \frac{h}{ce^2} \right)$

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(C) Let $\mu_0$ be related to $e, m, c,$ and $h$ as follows: $\mu_0 = k e^a m^b c^c h^d$.The dimensional formula for $\mu_0$ is $[M L T^{-2} A^{-2}]$.The dimensional formulas for the given quantities are: $e = [A T]$,$m = [M]$,$c = [L T^{-1}]$,and $h = [M L^2 T^{-1}]$.Substituting these into the equation:$[M L T^{-2} A^{-2}] = [A T]^a [M]^b [L T^{-1}]^c [M L^2 T^{-1}]^d$$[M L T^{-2} A^{-2}] = [M^{b+d} L^{c+2d} T^{a-c-d} A^a]$Comparing the powers of $M, L, T,$ and $A$ on both sides:$A: a = -2$$M: b + d = 1$$L: c + 2d = 1$$T: a - c - d = -2$Substituting $a = -2$ into the $T$ equation: $-2 - c - d = -2 \implies c + d = 0 \implies c = -d$.Substituting $c = -d$ into the $L$ equation: $-d + 2d = 1 \implies d = 1$.Since $d = 1$,then $c = -1$.Since $b + d = 1$,then $b + 1 = 1 \implies b = 0$.Thus,$\mu_0 \propto e^{-2} m^0 c^{-1} h^1 = \frac{h}{c e^2}$.

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

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