This is the 16289th most frequent Turkish word.
yapmayacağı
"Yapmayacağı" means "that he/she/it will not do."
Here, 'yapmayacağı' is used to indicate a future negative action ('wouldn't') related to homework.
Ev ödevini yapmayacağı için öğretmen ona kızdı.
The teacher got angry with her because she wouldn't do her homework.
In this case, 'yapmayacağı' expresses a commitment to abstain from certain actions ('would not').
Bu davranışları yapmayacağı konusunda kendisine söz verdi.
He promised himself that he would not engage in these behaviors.
Here, 'yapmayacağı' indicates an expected non-participation ('wouldn't join') in the context of the competition.