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 γ-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: (1) the optical variability is consistent with a pure red noise, for which the power spectral density can be well approximated by a single power law throughout the entire time domain probed; (2) the slope of power spectral density at high-energy γ-rays (∼1) is significantly flatter than that found at radio and optical frequencies (∼2) within the corresponding time variability range; (3) for the derived power spectra, we did not detect any low-frequency flattening, nor do we see any evidence for cutoffs 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 γ-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.