There are many synonyms for the phrase "three hundred years" that can be used interchangeably in writing and conversation. Some of these synonyms include "centuries", "tri-centennial period", "three centuries", "tercentenary cycle", "300-year span", "tricentennial era", and "three hundred year age". Each of these terms denotes a three-hundred year duration and can be used depending on the context in which it's being used. Regardless of which synonym you choose to use, it's essential to keep in mind that all these terms carry the same meaning and can be employed depending on the situation or the level of formality of the text.