In the word "unethical," the un-, ethic, and -al are all examples of morphemes.
Morphemes are the smallest units of meaning in a language. In this case, "un-" is a prefix (an affix), "ethic" is the root or base word, and "-al" is a suffix (another affix). So while "affixes" and "base words" are correct in specific contexts, the best general term that encompasses all three components is morphemes.