We present new Karl G. Jansky Very Large Array radio continuum images of the nuclei of Arp 220, the nearest ultra-luminous infrared galaxy. These new images have both the angular resolution to study the detailed morphologies of the two nuclei that power the galaxy merger and sensitivity to a wide range of spatial scales. At 33 GHz, we achieve a resolution of 0.081 x 0.063 and resolve the radio emission surrounding both nuclei. We conclude from the decomposition of the radio spectral energy distribution that a majority of the 33 GHz emission is synchrotron radiation. The spatial distributions of radio emission in both nuclei are well described by exponential profiles. According to the calculations, the nuclei of Arp 220 are only transparent in the frequency range ~5-350 GHz. Our results offer no clear evidence that an active galactic nucleus dominates the emission from either nucleus at 33 GHz.