A brief work of prose fiction is called

Short story

Explanation:

If it's a brief work, then it's usually a short story. However a prose fiction is usually a novel and there are different types of novel. When the prose is short we refer to it as a short story.

is there an image you meant to add?

explanation:

the sentence does not violate the phrase structure second rule (introduced by noam chomsky) because noun phrases consist of a determiner such as a, the or every, and a noun. in the sentence, the noun phrase the cake includes a determiner (the) and a noun (cake).

on the other hand, the first rule indicates that a sentence encloses a noun phrase, followed by a verb phrase. the example sentence can be analysed as follows:

john (n) + ate (v) + the (det) + cake (n).