die Ausübung
practice
The actual carrying out or practicing of an activity, profession, function, or office.
Die Ausübung seines Berufs als Arzt ist ihm sehr wichtig.
The practice of his profession as a doctor is very important to him.

exercise / practice
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practice
The actual carrying out or practicing of an activity, profession, function, or office.
Die Ausübung seines Berufs als Arzt ist ihm sehr wichtig.
The practice of his profession as a doctor is very important to him.

'Die Ausübung' (the exercise/practice) is the noun form of the verb 'ausüben' (to exercise/practice). The verb is made up of 'aus' and 'üben' and means to practically carry out an activity or function.
Er kann seinen Beruf wegen einer Krankheit zurzeit nicht ausüben.
He currently cannot practice his profession because of an illness.
The noun 'Ausübung' (exercise/practice) is very often followed by a genitive object that describes what is being exercised or practiced. Alternatively, the preposition 'von' with the dative can also be used.
Die Ausübung des Stimmrechts ist ein wichtiges demokratisches Prinzip.
The exercise of the right to vote is an important democratic principle.
The word 'Ausübung' (exercise/practice) belongs to formal language. You find it mainly in official, legal, or administrative texts.
Die freie Ausübung der Religion ist im Grundgesetz verankert.
The free exercise of religion is anchored in the Basic Law.
use
'die Verwendung' and 'die Ausübung' both have to do with something being used or done in practice. 'Verwendung' is especially suitable for things, means, words, or methods: you use something for a purpose. 'Ausübung' is more suitable for activities, professions, offices, rights, or power: you actively carry something out or practice it. They can be confused because both have to do with 'anwenden' (to apply / use). A simple rule of thumb is: things have a 'Verwendung', while activities or rights have an 'Ausübung'.

Für die Ausübung dieses Berufs braucht man viel Erfahrung.
You need a lot of experience to practice this profession.
Die Verwendung dieser App ist im Unterricht erlaubt.
The use of this app is allowed in class.