Q. I would like to know whether hyphenated words should always fall on the same line of a sentence. Is it OK to have the prefix at the end of one line and the rest of the word on the next line?
A. In printed materials it’s rarely possible to avoid hyphenating words at the end of all lines. In almost any book, you will see hyphens peppering the edge of the right margin. When a word must be hyphenated at the end of a line, it’s best to divide it at a logical location, such as after a prefix. You can read about word division involving prefixes at CMOS 7.40. More on word division is found at CMOS 7.36–47.