In English *exercise* doesn't change if it's used transitively or intransitively, but that's not the case for the Latin word it comes from. As Lewis and Short (and I'm sure other dictionaries) say, [*exerceo*](https://www.perseus.tufts.edu/hopper/morph?l=exerceo&la=la#lexicon) in the active means 'to exercise something,' whereas in the passive and used intransitively it means 'to exercise, practice, or train [oneself].'

Therefore if you had *exercet*, you would expect an object. See e.g. the first Cicero passage listed:

> me adolescentem multos annos...[Hortensius] exercuit, Cic. *Brut*. 64, 230 
>   
> Hortensius trained adolescent me for many years...

In your sentence, *exerceo* doesn't have an object or an agent, so you can assume it's being used in this intransitive sense, which is often called the 'middle voice.' Otherwise you might see *se* as an object of *exercet*, 'to exercise [oneself].'