Final answer:
The first Persian invasion of the Nile valley occurred in 671 BCE, while the second invasion happened in 525 BCE.
Step-by-step explanation:
The first Persian invasion of the Nile valley occurred in 671 BCE when king Esarhaddon of Assyria invaded Egypt and conquered both the Egyptian kingdom and northern Nubia. This invasion marked the first time in history that both the Nile valley and the Mesopotamian river valley were under the control of a single political entity. The second Persian invasion of the Nile valley happened in 525 BCE when Cambyses II, the son of Cyrus, invaded Egypt and successfully conquered it, adding it to the expanding Persian Empire.