Exaggerate is a verb.
"That's a nice story, Lisa, but please don't exaggerate."
Hyperbole means to exaggerate in the style of a figure of speech.
exaggerate, --d, --tion
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Personification
"Exaggerating" is a verb. It is the gerund form of the verb "to exaggerate".
Figure of speech
adjective
The word would be exaggerate.
THEY HAVE BOTH
The root word of "exaggerate" is "aggerare," which comes from the Latin word "adgerare" meaning "to heap up" or "to increase."
simile
Onomatopoeia