Final answer:
Teotihuacán's influence in the ancient Mesoamerican world is evidenced by its extensive trade network, the complex structures like the Pyramid of the Sun, its military and political interventions in Maya affairs, and its cultural legacies.
Step-by-step explanation:
The evidence that supports the conclusion that Teotihuacán wielded great influence in the larger Mesoamerican world during its height includes extensive trade networks, complex architectural designs, and the city's interactions with other civilizations. The wealth of Teotihuacán stemmed from trading in crafts, agricultural products, obsidian tools, cloth, and ceramics. Its influence is also seen through distinctive architectural monuments like the Pyramid of the Sun and the Pyramid of the Moon, as well as the Temple of Quetzalcoatl. Moreover, evidence from Maya sites suggests Teotihuacán intervened in Maya affairs, which included military interventions and possibly influencing political changes, such as a coup in the Maya city of Tikal in 378.
Moreover, the city was known to trade various goods such as obsidian, salt, cotton, and cacao, which were found across southern Mexico. Such extensive trade and cultural exchanges are indicative of Teotihuacán's reach and influence. Additionally, sculptures at sites like Monte Albán display the interaction of Teotihuacano diplomats with the Zapotec elite, demonstrating peaceful relations and influence between these civilizations. Even after Teotihuacán's decline, its cultural and religious legacies, like the worship of the Feathered Serpent, persisted and influenced subsequent civilizations including the Toltecs and the Aztecs.