The Aero Club operations chief reported that, the flight instructor and pilot were on a taxiway under air traffic control (ATC) instruction, the airplane encountered prop wash, originating from a larger (twin engine) turbine-powered airplane performing a maintenance engine(s) run-up. The maintenance run-up was performed in a location adjacent to the active taxiway. The light single-engine airplane was not told by ATC at any time during their taxi of the larger turbine-powered airplane's intentions. Subsequently, the light single-engine airplane was blown from its location while taxing behind the larger turbine-powered airplane, which resulted in substantial damage to the forward wing-spar. The Aero Club operations chief reported that there were no preimpact mechanical failures or malfunctions with the airframe or engine that would have precluded normal operation. The pilot of the larger turbine-powered airplane reported that, all requests for engine start, taxi, and high power runs were coordinated with ATC. He added that they had to reposition due to tailwinds, however a radio call was made to ATC and acknowledged that they had repositioned on the ramp to face into the wind. He added that he heard the light single-engine airplane receive a taxi clearance but did not hear any communications questioning the larger turbine-powered airplane's status or position with respect to any potential impact on aircraft taxiing behind them on the taxiway. He became aware of the light single-engine airplane's situation after the event when the pilot of the light single-engine airplane made a radio call to ground control.