Final answer:
The interactions between the Tang and Abbasid states positively affected both by enabling cultural exchange and trade. Despite the Battle of Talas halting further expansion, prior trade and cultural exchanges enriched both empires.
Step-by-step explanation:
The interactions between the Tang and Abbasid states positively affected both states by promoting cultural exchange and trade. These interactions led to a significant cultural impact on the Tang Empire, as whole communities of merchants from the former Sasanian Empire moved to the Tang capital, bringing a range of exotic products and luxury goods. Moreover, the trade relations fomented the development of an international culture within Tang China's major cities. The Abbasid Caliphate was also positively influenced, as their geographic positioning after moving their capital to Baghdad allowed them to streamline their dominance of the Silk Roads.
Despite ultimately halting further expansion through the Battle of Talas River in 751, where Tang forces were defeated by the Abbasids and their allies, the engagement and preceding interactions had already facilitated a period of extensive cultural and commercial exchange between the two empires. These interactions undoubtedly enriched both the Tang and Abbasid states, leading to an increased flow of goods, ideas, and cultural practices.