Which term describes the act of leaving the army without permission?

The term that describes the act of leaving the army without permission is "desert." In military terminology, desertion refers specifically to a service member abandoning their duty or failing to report for service without authorization. This violation of military law is considered a serious offense and can have significant legal consequences.

Other terms in the options do not align with the concept of leaving the army improperly. For example, "exemption" refers to being free from an obligation or duty, often due to specific circumstances or criteria, which does not pertain to the act of leaving without permission. "Draft" involves the conscription or selection of individuals into military service, which is the opposite of leaving the service. "Penalty" generally refers to the consequence imposed for breaking a law or rule but does not specifically describe the act of leaving the military without permission. Thus, "desert" is the most accurate term in this context.