The correct answer is B) It is the same or in a direct relationship through reduction gears. In a single shaft, cold-end drive gas turbine, the power output speed is directly related to the speed of the compressor through reduction gears. The compressor speed determines the speed of the turbine, which in turn drives the output shaft. The reduction gears then convert the high turbine speed to the desired lower power output speed, maintaining a direct relationship between the compressor and power output speeds. The other options are incorrect because option A would indicate an independent relationship, which is not the case, while options C and D do not accurately describe the speed relationship in this type of gas turbine system.