Which method of gear rotation would typically result in the slowest operation for a given gear ratio?

The option indicating low speed is correct because, with respect to gear rotation, low-speed operation inherently means that the rotational velocity of the gears is decreased. When analyzing gear systems, the speed at which the output gear turns is inversely related to the gear ratio. A lower speed setting will yield fewer rotations of the output gear for each rotation of the input gear, which typically results in slower operation at a given gear ratio.

In contrast, high-speed settings typically produce faster rotations of gears due to the input gear turning rapidly. Variable speed allows for adjustments depending on the setting, which implies that it could be either fast or slow but does not guarantee the slowest operation. Constant speed means that the speed does not change over time, but it does not inherently imply a slower or faster operation in comparison to low speed. Therefore, among these options, low speed definitively corresponds to the slowest operation for a specified gear ratio, making it the most accurate choice.