  We study AC electric($\sigma$), thermoelectric($\alpha$), and
thermal($\bar{\kappa}$) conductivities in a holographic model, which is based
on 3+1 dimensional Einstein-Maxwell-scalar action. There is momentum relaxation
due to massless scalar fields linear to spatial coordinate. The model has three
field theory parameters: temperature($T$), chemical potential($\mu$), and
effective impurity($\beta$). At low frequencies, if $\beta < \mu$, all three AC
conductivities($\sigma, \alpha, \bar{\kappa}$) exhibit a Drude peak modified by
pair creation contribution(coherent metal). The parameters of this modified
Drude peak are obtained analytically. In particular, if $\beta \ll \mu$ the
relaxation time of electric conductivity approaches to $2\sqrt{3} \mu/\beta^2$
and the modified Drude peak becomes a standard Drude peak. If $\beta > \mu$ the
shape of peak deviates from the Drude form(incoherent metal). At intermediate
frequencies($T<\omega<\mu$), we have analysed numerical data of three
conductivities($\sigma, \alpha, \bar{\kappa}$) for a wide variety of
parameters, searching for scaling laws, which are expected from either
experimental results on cuprates superconductors or some holographic models. In
the model we study, we find no clear signs of scaling behaviour.
