  We present 7mm Very Large Array continuum images of the starburst galaxy M82.
On arcsecond scales, two-thirds of the 7mm continuum consists of free-free
emission from HII regions. In the subarcsecond resolution map, we identify 14
compact sources, including 9 bright HII regions with N_Lyc > 10^51 sec^-1. Four
of the HII regions have rising spectra, implying emission measures > 10^8 cm^-6
pc. Except for one compact source with peculiar features, all other compact
radio sources are found in dust lanes and do not have optical or near-infrared
continuum counterparts. Four regions of extended, high brightness (EM > 10^7
cm-6 pc) radio emission are found in our high resolution map, including some as
large as ~2", or 30 pc, representing either associations of small HII regions,
or sheetlike structures of denser gas. The good correlation between 7 mm
emission and Spitzer IRAC 8 micron continuum-removed PAH feature suggests that
PAH emission may track the recently formed OB stars. We find an excellent
correlation between molecular gas and star formation, particularly dense gas
traced by HCN, down to the ~ 45 pc scale in M82. We also find star formation
efficiencies (SFEs) of 1-10% on the same scale, based on CO maps. The highest
SFE are found in regions with the highest dense gas fractions.
