The modal verb 能 is used in the following cases:
1) when there is an opportunity to do an act, i.e. it is either physically possible, or circumstances allow it to be done.
A computer can perform multiple operations at the same time
diànnǎo néng tóngshí zuò duō xiàng gōngzuò
My phone is out of battery, so I can't call him
wǒ de shǒujī méi diàn le, wǒ bù néng gěi tā dǎ diànhuà
The negative form of modal verbs is formed by adding the adverb 不 . The adverb 没 cannot be used.
2) something is being done well.
The adverbs such as 很 or 最 are often placed before the verb 能.
In this meaning it is similar to the modal verb 会 .
Hainan Island attracts the most tourists
hǎinán dǎo zuì néng xīyǐn yóukè
This food is very filling (That is, you easily get full from eating this food)
zhè zhòng cài hěn néng tián bǎo dùzi
3) there is an inanimate object that has some function. 能 is used to emphasize this function.
X-rays can penetrate many objects
x-shèxiàn néng chuān tòu hěn duō wùtǐ
4) the action is permitted by the rules of conduct.
Can I ask a question?
wǒ néng tí ge wèntí ma
5) the action seems reasonable to the speaker.
We can patch up those holes
wǒmen néng bǔ shàng nà xiē lòudòng
You can use 可以 to give a short positive answer to a question with 能.
不能 and 不行 are used to give a short negative answer to a question with 能.
Can you leave earlier? — Yes, I can
nǐ néngbunéng zǎodiǎn chūqù — kěyǐ
Can you leave earlier? — No, I can't
nǐ néngbunéng zǎodiǎn chūqù — bù néng
The verb 能够
The verb 能够 is most often used in the written language.
能够 and 能 have differences only in usage.
The ceiling and wall lights can be controlled independently
tiānhuābǎn hé qiáng shàng de dēng nénggòu dúlì cāokòng
I promise she will work hard
wǒ bǎozhèng tā nénggòu nǔlì gōngzuò
You can use 不能够 in a negative answer to a question with 能够.
A positive answer to a question with 能够 must be detailed.
An answer with 能够 cannot be short.
The verb 可以
The modal verb 可以 is used in the following cases:
1) when it expresses the ability of an object to do an action. It is translated as "can".
It is often used in compound sentences that contain certain conditions for doing an action.
The modal verbs 可以 and 能 are used almost interchangeably.