“Beth-aven.” “Beth-aven” means “House of Wickedness,” and was a derogatory term the prophet used for the town of Bethel (Beth-el), which means “House of God,” but which had the golden calf idol that Jeroboam had made. See commentary on Hosea 4:15.
“it will be taken from them into exile.” It was a common custom for a conquering nation to take back home with them the gods of the defeated nation, as we see here in Hosea 10:5 (cp. Isa. 46:1-2; Jer. 48:7; 49:3; Dan. 11:8), and this was especially true if they were made of valuable metals. When Nebuchadnezzar king of Babylon conquered Judah, he took away the Temple vessels, because they were valuable but also because there wasn’t any god in the Temple to take away to show that the God of Judah had been defeated (2 Kings 24:13; 25:13-15; 2 Chron. 36:7, 18). When the Assyrians conquered Israel, they took the golden calves of Israel back to Assyria with them.
The literal Hebrew is that the calf “had been taken from them,” using the prophetic perfect idiom to express a future certainty.
[For more on the prophetic perfect, see commentary on Eph. 2:6.]