Sparta was finally able to defeat Athens at the end of the Peloponnesian war by doing what?

Sparta was able to defeat Athens at the end of the Peloponnesian War by forming an alliance with Persia, which provided financial support to build a powerful navy. This allowed Sparta to challenge Athenian naval supremacy and ultimately secure key victories, such as the decisive Battle of Aegospotami in 405 BCE. Additionally, Sparta's strategy involved cutting off Athenian supply lines and exploiting internal discord within Athens, leading to the city's eventual surrender in 404 BCE.