cackle vs let out

cackle is a noun but let out is not a noun.

Word	Noun	Adjective	Verb	Adverb
cackle	Yes	No	Yes	No
let out	No	No	Yes	No

As verbs, let out is a hypernym of cackle; that is, let out is a word with a broader meaning than cackle:

Other hypernyms of cackle include emit, let loose, utter.

cackle (noun)	let out (noun)
a loud laugh suggestive of a hen's cackle
noisy talk
the sound made by a hen after laying an egg

cackle (verb)	let out (verb)
emit a loud, unpleasant kind of laughing	make (clothes) larger
squawk shrilly and loudly, characteristic of hens	make known to the public information that was previously known only to a few people or that was meant to be kept a secret
talk or utter in a cackling manner	express audibly; utter sounds (not necessarily words)
make a noise characteristic of a goose	bring out of a specific state