The classical form of the verb 食べる is 食ぶ. It belongs 下二段活用動詞; shimonidan conjugation verbs, and conjugates like 食べぬ/食べうる/食ぶ/食ぶる/食ぶれば/食べよ. Thus, as you can see, the stem is 食, not 食べ.
That's a quite understandable question.
Many natives also use that rule to figure out what part of the verb the 送り仮名 is, but there are some exceptions like this.