Exodus 1:8-11 give us an idea of which Pharoah was ruling at the time. It matches with the first of the Hyksos rulers in Egypt. This book begins after Joseph died and a Pharoah rose up who did not know him and oppressed the Israelites within Egypt. The book ends with the setting up of the Tabernacle in Exodus 40, which occurred in 1444 BC. We do not know when the book was written, as it could have been written at any point between the Exodus and Moses death in 1406. Some have suggested it was most likely written between 1446-1444 BC, but this is not directly stated anywhere, and we cannot know if Moses wrote Exodus at one time or at multiple times and when he wrote it in comparison with the rest of the Pentateuch.