IPA: /ˈkæv.əˌlɪr.li/
KK: /ˈkævəˌlɪrli/
In a way that shows a lack of concern or seriousness; casually or dismissively.
He cavalierly dismissed her concerns about the project.
Cavalierly → It is formed from "cavalier" (from Old French *cavalier*, meaning horseman or knight) and the suffix "-ly" (meaning in a manner of). The word "cavalierly" means in a manner that is dismissive or showing a lack of concern, akin to the attitude of a knight who is unconcerned with trivial matters.
Think of a 'knight' ('cavalier') who acts 'in a manner' ('-ly') that is carefree or dismissive — that's why cavalierly means to act without concern.