IPA: /ˈpɜːrpəs.ləs.li/
KK: /ˈpɜr.pəs.ləs.li/
In a way that lacks purpose or intention.
He wandered purposelessly through the empty streets, unsure of where to go.
Purposelessly → It is formed from "purpose" (from Old French *porpos*, meaning intention or aim) and "-less" (meaning without) and "-ly" (meaning in a manner). The word "purposelessly" means in a manner that is without intention or aim.
Think of being 'without' ('-less') a 'goal' ('purpose') — that's why purposelessly means acting without any intention.