We analyze the multifrequency radio spectral properties of 41 6GHz-detected Atacama Large Millimeter/submillimeter Array(ALMA)-identified, submillimeter galaxies (SMGs), observed at 610 MHz,1.4 GHz, and 6 GHz with the Giant Metrewave Radio Telescope and the VeryLarge Array. Combining high-resolution (∼0.″5) 6 GHz radio andALMA 870 μm imaging (tracing rest frame ∼20 GHz, and ∼250μm dust continuum), we study the far-infrared/radio correlation viathe logarithmic flux ratio q IR, measuring <{q}IR}> =2.20+/- 0.06 for our sample. We show that thehigh-frequency radio sizes of SMGs are ∼1.9 ± 0.4×(∼2–3 kpc) larger than those of the cool dust emission, andfind evidence for a subset of our sources being extended on ∼10 kpcscales at 1.4 GHz. By combining radio flux densities measured at threefrequencies, we can move beyond simple linear fits to the radio spectraof high-redshift star-forming galaxies, and search for spectralcurvature, which has been observed in local starburst galaxies. At leasta quarter (10/41) of our sample shows evidence of a spectral break, witha median <{α }610 {GHz}1.4 {GHz}>=-0.60+/- 0.06, but <{α }1.4 {GHz}6{GHz}> =-1.06+/- 0.04—a high-frequency flux deficitrelative to simple extrapolations from the low-frequency data. Weexplore this result within this subset of sources in the context ofage-related synchrotron losses, showing that a combination of weakmagnetic fields (B ∼ 35 μG) and young ages (t SB ∼40–80 Myr) for the central starburst can reproduce the observedspectral break. Assuming these represent evolved (but ongoing)starbursts, and we are observing these systems roughly halfway throughtheir current episode of star formation, this implies starburstdurations of ≲100 Myr, in reasonable agreement with estimatesderived via gas depletion timescales.