Material moduli of the cytoskeleton (CSK) influence a wide range of cell functions. There is substantial evidence from reconstituted F-actin gels that a regime exists in which the moduli scale with frequency with a universal exponent of 3/4. Such behaviour is entropic in origin and is attributable to fluctuations in semiflexible polymers driven by thermal forces, but it is not obvious a priori that such entropic effects are responsible for the elasticity of the CSK. Here we demonstrate the existence of such a regime in the living cell, but only at high frequencies. Fast events scaled with frequency in a manner comparable to semiflexible-polymer dynamics, but slow events scaled with a non-universal exponent that was systematically smaller than 3/4 and probably more consistent with a soft-glass regime. These findings strongly suggest that at smaller timescales elasticity arises from entropic fluctuations of a semiflexible-filament network, whereas on longer timescales slow (soft-glass-like) dynamics of a different origin prevail. The transition between these two regimes occurred on timescales of the order of 0.01 s, thus setting within the slow glassy regime cellular events such as spreading, crawling, contracting, and invading.