authority vs last word

authority and last word both are nouns.

Word	Noun	Adjective	Verb	Adverb
authority	Yes	No	No	No
last word	Yes	No	No	No

As nouns, last word is a hyponym of authority; that is, last word is a word with a more specific, narrower meaning than authority:

authority (noun)	last word (noun)
the power or right to give orders or make decisions	elegance by virtue of being fashionable
official permission or approval	the final statement in a verbal argument
freedom from doubt; belief in yourself and your abilities	an authoritative statement
an authoritative written work
an administrative unit of government
an expert whose views are taken as definitive
(usually plural) persons who exercise (administrative) control over others