The flight instructor of a light single-engine airplane reported that while he and the student pilot were on a taxiway under air traffic control (ATC) instruction, the airplane encountered prop wash, originating from a larger (four 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 that was authorized for parking as well as 80% engine(s) power run-ups. The larger turbine-powered airplane was the third in a row a five, of like model airplanes being parked at the location. The light single-engine airplane was not on frequency when the larger turbine-powered airplane was given the clearance, and 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 approximately 80 feet from its original location while taxing behind the larger turbine-powered airplane, which resulted in substantial damage to the firewall. The flight instructor reported that there were no pre impact mechanical failures or malfunctions with the airframe or engine that would have precluded normal operation. As a safety recommendation the flight instructor stated that the incident could have been prevented with better communications between the tower controllers and the larger turbine-powered airplane's ground personnel.