
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.

exercise
The application or use of power, influence, control, or a right.
Die Ausübung von politischer Macht erfordert große Verantwortung.
The exercise of political power requires great responsibility.
'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.
execution / version
Ausführung means the specific carrying out of a plan, assignment, or individual operation. Ausübung, by contrast, refers to practicing an activity or performing a profession, function, or official role. An assignment is ausgeführt, while a professional or official role is ausgeübt.

Die Architektin braucht für die Ausübung ihres Berufs viel Fachwissen.
The architect needs extensive specialist knowledge to practice her profession.
Die Architektin überwacht die sorgfältige Ausführung des Bauauftrags.
The architect oversees the careful execution of the construction assignment.