We present the results of an observational campaign which obtained high time cadence, high precision, simultaneous optical and IR photometric observations of three M dwarf flare stars for 47 hours. The campaign was designed to characterize the behavior of energetic flare events, which routinely occur on M dwarfs, at IR wavelengths to milli-magnitude precision, and quantify to what extent such events might influence current and future efforts to detect and characterize extrasolar planets surrounding these stars. We detected and characterized four highly energetic optical flares having U-band total energies of ~7.8x10^30 to ~1.3x10^32 ergs, and found no corresponding response in the J, H, or Ks bandpasses at the precision of our data. For active dM3e stars, we find that a ~1.3x10^32 erg U-band flare (delta Umax ~1.5 mag) will induce <8.3 (J), <8.5 (H), and <11.7 (Ks) milli-mags of a response. A flare of this energy or greater should occur less than once per 18 hours. For active dM4.5e stars, we find that a ~5.1x10^31 erg U-band flare (delta Umax ~1.6 mag) will induce <7.8 (J), <8.8 (H), and <5.1 (Ks) milli-mags of a response. A flare of this energy or greater should occur less than once per 10 hours. No evidence of stellar variability not associated with discrete flare events was observed at the level of ~3.9 milli-mags over 1 hour time-scales and at the level of ~5.6 milli-mags over 7.5 hour time-scales. We therefore demonstrate that most M dwarf stellar activity and flares will not influence IR detection and characterization studies of M dwarf exoplanets above the level of ~5-11 milli-mags, depending on the filter and spectral type. We speculate that the most energetic megaflares on M dwarfs, which occur at rates of once per month, are likely to be easily detected in IR observations with sensitivity of tens of milli-mags.
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