Did Cleopatra rule Egypt while George Washington was the president of the U.S.?

No, Cleopatra did not rule Egypt while George Washington was President of the United States. Cleopatra VII, the last active ruler of the Ptolemaic Kingdom of Egypt, died in 30 BC, while George Washington served as president from 1789 to 1797. There is a significant gap of over 1,700 years between their respective times of influence.