Nanoscale semiconductor materials have been extensively investigated as the channel materials of transistors for energy-efficient low-power logic switches to enable scaling to smaller dimensions. On the opposite end of transistor applications is power electronics for which transistors capable of switching very high voltages are necessary. Miniaturization of energy-efficient power switches can enable the integration with various electronic systems and lead to substantial boosts in energy efficiency. Nanotechnology is yet to have an impact in this arena. In this work, it is demonstrated that nanomembranes of the wide-bandgap semiconductor gallium oxide can be used as channels of transistors capable of switching high voltages, and at the same time can be integrated on any platform. The findings mark a step towards using lessons learnt in nanomaterials and nanotechnology to address a challenge that yet remains untouched by the field.