Unit Conversion Formula

Rarely Tested

If $$[Q] = [M^a L^b T^c]$$ and units relate as $$M_2 = k_1 M_1$$, $$L_2 = k_2 L_1$$, $$T_2 = k_3 T_1$$, then:

$$Q_2 = Q_1 \cdot (k_1)^a \cdot (k_2)^b \cdot (k_3)^c$$
Question 1

In a new system of units, the units of mass, length, time and current are $$5\,\mathrm{kg}$$, $$5\,\mathrm{m}$$, $$5\,\mathrm{s}$$ and $$5\,\mathrm{A}$$, respectively. If $$\mu_0$$ and $$\epsilon_0$$ are the permeability and permittivity of free space, respectively, then in this new system of units, the magnitude of one SI unit of $$\sqrt{\mu_0/\epsilon_0}$$, is:

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