The correct option is A Smiling mischievously
A participle is a verb form that ends in -ing or -ed (present
participles end in ing and typically, past participles end in ed) and
functions as an adjective, as it modifies a noun. A participial phrase
consists of a participle and other words, like a preposition a noun, and so on. In the given sentence, "smiling" is a participle and it is followed by an adverb "mischievously"; this is a participial phrase as it modifies the pronoun "she". Hence option A is correct. "She ate" is a phrase made of the subject and verb, respectively; it does not contain a participle, hence option B is incorrect. "Ate another" is a phrase made up of a verb and determiner, respectively; since it does not contain a participle, option C is incorrect. "Piece of cake" is a noun phrase, made up of two nouns and a preposition "of", hence option D is incorrect.