Joseph called his brothers down to Egypt to be with him, where he'd become favored by the pharaoh (who isn't named in the Bible), and all of his father Jacob's family remained there through the times of famine which he'd foretold. Their descendents came to be large tribes who settled into the land of Goshen east of the Nile delta; while about 400 years went by.
In the century of the 1300s BC, a pharaoh who called himself Akhenaten, abetted by his beautiful and famous queen Nefertiti, tried to impose a change of religion upon the whole nation of Egypt: forcing the people to worship only the sun god and disregard the many others that had become popular. After this pharaoh and his oldest son and successor Smenkhare, had died, his younger son was slowly persuaded by his advisors to change his name from Tutankhaten to Tutankhamon and restore the old ways of worship. However, this pharaoh then died as a young man, and since there was no direct claimant, the commander of the army in northern Egypt, named Horemheb, was supported by the boy king's vizier Ay to assume the throne - very likely to keep any of the other family members who might insist on going back to the odd ways of their ancestor from gaining power.
During this period of upheaval in Egypt, some of the foreign possessions that had been subjugated by earlier kings saw their chance to regain independence and refused to pay further tribute. Horemheb determined to act to put down the rising rebellions, and moved his capital away from the religious center at Thebes up to the trading center of Memphis in the delta. He had no sons, so he made another officer of the Egyptian military in the northern area, named Ramses, his coregent to rule while he was away fighting.
Horemheb had relocated the capital closer to the place he called home in order to better marshal and maneuver the army, as well as to wrest authority away from the potential interference of the priests. And although primarily his efforts in civic improvements and grand architecture were focused in the traditional southern area and the Theban temple complex, where he began the construction of the grand hypostyle hall at Karnak, he started to undertake some building projects nearby (and even though he was eventually buried in the Valley of the Kings as befitting a pharaoh, an elaborate tomb which he'd had constructed at Saqqara near Memphis was unearthed in 1975). Due to the combination of the return of ideologic stability & identity, increased military presence and political influence in the north, distrust of foreign loyalties, and intensive local expansion of national building, it's possible that it was about this time that the Hebrews began to be oppressively conscripted as laborers, if not earlier.
Although Horemheb campaigned successfully, he still had no sons to succeed him when he died; and by the time the also- elderly Ramses I became pharaoh he ruled for only a year or so before he died as well. But this meant that the son of Ramses I, named Seti, was well matured upon becoming pharaoh, and capably continued to both expand the empire and govern the recovering nation.
Seti, as depicted in the movie The Ten Commandments, also stepped up the scale and pace of building throughout the country as a means of developing and exhibiting national pride; while he sought to institute a new array of temples around the northern capital. His young son, named Ramses II in honor of Seti's father, was brought up to command at an early age, and held the rank of (trainee) captain in the army when he was just 10 years old. Later, when the expeditions of the Egyptian army had returned laden with spoils, the Hebrews were pressed into building the treasure cities mentioned in the Bible, that included Ramses' own choice of residence: the fabled lost city of Piramis (egyptian Pi- Ramesses= "house of Ramses", or in scripture Raamses).
Ramses II became known as Ramses the Great partly through his own efforts at publicity. He made sure that the story of his valiant stand with just his household guards against a surprise attack from a Hittite force at the siege of Kadesh was published and repeated throughout the kingdom. He maintained an enormous harem and supposedly had in the neighborhood of 100 children; although he appears to have honored his queen, named Nefertari, enough to carve out two megalithic temples at Abu Simbel: one for him and one for her. Along the same lines, his dedication to the completion of his predecessors' colossal temple structures was augmented by his building of the Ramasseum; so people would be able to worship him along with the other gods.
There is debate over whether Ramses, who was pretty clearly a pharaoh of the oppression of the Hebrews, was the pharaoh of the exodus, or whether it was his successor Merneptah. Unfortunately, again the Bible doesn't specify which pharaoh's daughter it was that pulled Moses out of the Nile. Merneptah was Ramses' 13th son, but Ramses ruled so long that he was the next in line still living at age 60 when Ramses was entombed in the Valley of the Kings. Sometime rather early in his reign, his army went to suppress a revolt in Palestine, and it was recorded on a block of stone which was termed the "Israel Stela" when it was discovered, because it contains the first known reference to the people of Israel; though not necessarily the state of Israel.