Final answer:
The outcome of the Battle of Ayacucho in 1824 was a significant victory for the independence movements in South America.
Step-by-step explanation:
The outcome of the Battle of Ayacucho in 1824 was a significant victory for the independence movements in South America. The battle took place between the Spanish royalist forces and the revolutionary forces led by Antonio José de Sucre. Despite being outnumbered, Sucre's forces emerged victorious, resulting in the collapse of Spanish control in South America. This outcome marked a major turning point in the struggle for independence in the region.