What did the Jews establish in the cities of the Roman Empire where they settled?
Throughout the Roman Empire, in cities of any notable population, the Jews established businesses and synagogues, and other such institutions. Their long migration from Babylon scattered them across the then-known world, so they formed settled communities wherever they went, which explains the Jews present at Pentecost.
Les explains that the Jews had been taken out to Babylon, and instead of returning to Jerusalem, they scattered throughout the then-known world. They became comfortable in the Gentile world and astute at banking and business. Wherever there was a city of any population of note, Jews established businesses and synagogues, and what have you, everywhere throughout the whole Roman Empire. This historical background makes Acts chapter 2, verse 5, understandable: devout Jews, keepers of the Law and temple worshipers, were dwelling at Jerusalem for Pentecost, having come out of every nation under heaven because their people had been scattered across the known world.