underestimate vs underrate

underestimate is a noun but underrate is not a noun.

Word	Noun	Adjective	Verb	Adverb
underestimate	Yes	No	Yes	No
underrate	No	No	Yes	No

As verbs, underestimate and underrate are synonyms defined as:

underestimate (noun)	underrate (noun)
an estimation that is too low; an estimate that is less than the true or actual value

underestimate (verb)	underrate (verb)
make a deliberately low estimate	make too low an estimate of
make too low an estimate of
assign too low a value to