= Solution
Rearrange the Arrhenius relation using the molar <activation energy> and the <molar gas constant>:
$$
\begin{aligned}
A&=k_3\exp\left(\frac{E_a}{RT}\right)\\
&=(1.933\times10^{-14})\exp\left(\frac{4905}{8.3145\times298}\right),\\
\boxed{A}&=\boxed{1.400\times10^{-13}\,\mathrm{dm^3\,molecule^{-1}\,s^{-1}}}.
\end{aligned}
$$
The exponent is dimensionless. There is no Avogadro factor in it because both $E_a$ and $R$ are expressed per mole; the molecular <concentration> convention only determines the units of the prefactor.
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