Final answer:
The synonym for 'exert' fitting the context of Mao Zedong's speech is 'employ', which both indicate using something effectively for a specific purpose.
Step-by-step explanation:
The best synonym for the word exert as used in the excerpt from Mao Zedong’s speech "Serve the People" is employ. In the context of the speech, Mao urges for a committed effort or use of force in the struggle to save the Chinese people. The term 'exert' implies putting to use or applying an ability or influence effectively. Therefore, 'employ' suits the context as it connotes the act of using something for a particular purpose, which aligns with how 'exert' is intended in the speech.
The other options, such as 'keep', 'hurt', and 'try' do not capture the essence of the word 'exert' in this context. 'Keep' would suggest maintaining a state or condition, 'hurt' would signify causing pain or harm, which are not related to the application of effort directed towards an objective, and 'try' suggests an attempt, which lacks the connotation of an effective action that 'exert' carries.