We present the results of our power spectral analysis for the BL Lac object PKS 0735+178 utilizing the Fermi-LAT survey at high-energy $gamma$-rays, several ground-based optical telescopes, and single-dish radio telescopes operating at GHz frequencies. The novelty of our approach is that, by combining long-term and densely sampled intra-night light curves in the optical regime, we were able to construct for the first time the optical power spectrum of the blazar for a time domain extending from 23 years down to minutes. Our analysis reveals that: (i) the optical variability is consistent with a pure red noise, for which the power spectral density can well be approximated by a single power-law throughout the entire time domain probed; (ii) the slope of power spectral density at high-energy $gamma$-rays ($sim 1$), is significantly flatter than that found at radio and optical frequencies ($sim 2$) within the corresponding time variability range; (iii) for the derived power spectra we did not detect any low-frequency flattening, nor do we see any evidence for cut-offs at the highest frequencies down to the noise floor levels due to measurement uncertainties. We interpret our findings in terms of a model where the blazar variability is generated by the underlying single stochastic process (at radio and optical frequencies), or a linear superposition of such processes (in the $gamma$-ray regime). Along with the detailed PSD analysis, we also present the results of our extended (1998-2015) intra-night optical monitoring program and newly acquired optical photo-polarimetric data for the source.
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