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The recent discovery of the seven planet TRAPPIST--1 system comma including three habitable zone planets comma has opened up a new avenue for studying temperate terrrestrial planets comma with potentially habitable atmospheres. This system and others like it around the lowest-mass stars will be prime targets for both planet searches and studies to directly characterize the atmospheres of Earth-sized exoplanets. Understanding these atmospheric observations and the potential prospect of such exoplanets to develop and sustain life critically depends on the high-energy stellar radiation environment from X-ray to ultraviolent wavelengths because of the ability of this emission to drive atmospheric mass-loss comma and it.s strong influence on planetary photochemistry comma including its ability to catalyze prebiotic chemical pathways. However comma little is known about the X-ray to UV radiation field of stars at the end of the main sequence. We propose a survey of the joint X-ray and UV emission of a sample of M7-M9 dwarfs comma to provide the basis for estimating the high-energy stellar radiation environment around these stars across a range of activity levels comma and to use these spectral observations as inputs to planetary photochemsitry models. Furthermore comma these observations will probe the nature of chromospheric and coronal heating in the coolest stellar atmospheres.