Select the most more appropriate option to fill in the blank.

If you fail to ______ your authority properly, they will remove you.

exercise

The most appropriate option to fill in the blank is exercise.

The sentence "If you fail to exercise your authority properly, they will remove you" means that if you do not use your authority in the correct way, you will be removed from your position. The word "exercise" is the most appropriate word to use in the blank because it accurately reflects the fact that authority is something that needs to be used, not just known or managed.

The other options are not as appropriate.

• The word "know" is used to talk about having knowledge of something. This does not make sense in the context of the sentence, as the speaker is not talking about having knowledge of authority, but about using authority in the correct way.
• The word "manage" is used to talk about controlling or overseeing something. This does not make sense in the context of the sentence, as the speaker is not talking about controlling or overseeing authority, but about using authority in the correct way.
• The word "demand" is used to talk about asking for something forcefully. This does not make sense in the context of the sentence, as the speaker is not talking about asking for authority, but about using authority in the correct way.