Which power did farmers, merchants, and artisans eventually gain in the Roman republic

The correct answer is that farmers, merchants, and artisans gained the power to elect officials who would then be able to veto laws harmful to these people. Since these groups of people did not belong to the nobility (instead they belonged to what is known as the plebeian majority), they had no say in laws, until they were able to elect these officials.

In the Roman Republic, farmers, merchants and artisans eventually gained the power to elect tribunes who represented them in government and could veto the actions of consuls and other leaders, protecting the interests of the common people (the "plebeians") whom they represented.

"Tribunis Plebis" was the Latin term for "Tribune of the people" (the plebs). "Concilium Plebis" was the Latin name for the Plebeian Council or assembly. There had been assemblies of the plebeians before plebeian unrest that reached a crisis stage in 494 BC. But after that date, plebeian assembly's actions, under the authority of the tribune of the people, carried more official authority. The creation of the office of tribune, to represent the people and offset the power of the consul, occurred after major conflict between the plebeians and the ruling class (the patricians) in 495-494 BC.