The power-lawshape of the power spectral density (PSD) of blazar light curves-P(V_k) α V_k ^-β _k, where V_k is the temporal frequency-indicates that blazar variability is, in general, of the colored-type noise (β ≃ 1-3). A precise characterisation of PSD slopes, normalizations, or characteristic timescales (if any) manifesting as distinct features in the power spectra of blazars is important for constraining the physics of the emission and energy dissipation processes in relativistic jets. Here we present the results of the PSD analysis for the BL Lac object PKS 0735+178 at GeV (Fermi-LAT), optical (R-band), and radio (GHz band from UMRAO and OVRO programmes) frequencies, covering a broad range in variability timescales. The novelty of our approach is that in the optical regime, by combining the long-term and densely sampled R-band intra-night light curves, we constructed the PSD for time periods ranging from 23 years down to minutes. Our analysis reveals that: (1) the nature of processes generating flux variability at optical and radio frequencies is different from those operating at GeV photon energies (β ~ 2 and 1, respectively); (2) the main driver behind the optical variability is the same on timescales of years, months, days, and hours (a single power-law with β ~ 2). We discuss our findings in the framework of a model where the overall blazar variability is generated by an underlying single stochastic process (radio and optical frequencies), or a linear superposition of such processes (γ -ray regime).