We examine the bright radio synchrotron counterparts of low-luminosity gamma-ray bursts (llGRBs) and relativistic supernovae (SNe) and find that they can be powered by spherical hypernova (HN) explosions. Our results imply that radio-bright HNe are d
riven by relativistic jets that are choked deep inside the progenitor stars or quasi-spherical magnetized winds from fast-rotating magnetars. We also consider the optical synchrotron counterparts of radio-bright HNe and show that they can be observed as precursors several days before the SN peak with an r-band absolute magnitude of M_r ~ -14 mag. While previous studies suggested that additional trans-relativistic components are required to power the bright radio emission, we find that they overestimated the energy budget of the trans-relativistic component by overlooking some factors related to the minimum energy of non-thermal electrons. If an additional trans-relativistic component exists, then a much brighter optical precursor with M_r ~ -20 mag can be expected. Thus, the scenarios of radio-bright HNe can be distinguished by using optical precursors, which can be detectable from < 100 Mpc by current SN surveys like the Kiso SN Survey, Palomar Transient Factory, and Panoramic Survey Telescope & Rapid Response System.
