Final answer:
The Neo-Babylonian Empire expanded through trade and scientific advancements, specifically in astronomy and mathematics, which also supported their merchants and administration. Their focus on economic strategies rather than just conquest led to their prosperity until their eventual fall to Cyrus the Great's Persian Empire.
Step-by-step explanation:
The Neo-Babylonian Empire expanded its territories not only through conquest but also through trade. Unlike their Assyrian predecessors, the Babylonians focused on economic expansion by building new roads and canals to facilitate long-distance trade. They encouraged commerce throughout their empire and even during times of war with Egypt, Egyptian merchants were allowed to do business within the empire. This economic strategy contributed significantly to the wealth of the Neo-Babylonian kingdom, leading to prosperous times and the construction of monumental architecture, such as the Hanging Gardens of Babylon, one of the Seven Wonders of the Ancient World.
The empire also benefited greatly from the scientific advancements in areas like astronomy and mathematics. This not only brought cultural enrichment but also practical applications that supported navigation and timekeeping, which were essential for trade and administration of the empire. It is noteworthy that the Neo-Babylonian Empire, with its capital in Babylon, ultimately fell to Cyrus the Great of Persia in 539 BCE, who incorporated its territories into the vast Persian Empire.