Questions & Answers about Её улыбка выражает радость.
Because её means her in the possessive sense: her smile.
- она = she
- её = her
So:
- она улыбается = she is smiling
- её улыбка = her smile
In this sentence, её is showing possession, so её is the correct word.
Улыбка is in the nominative case because it is the subject of the sentence — the thing doing the action.
In Её улыбка выражает радость, the smile is what expresses the joy.
So:
- улыбка = subject
- subject in Russian usually takes the nominative
That is why it stays as улыбка.