take care ofThe て-form of 面倒をみる, used to connect to another expression or to make a request, such as 面倒をみてください (please take care of). Depending on context, it can mean looking after someone or something, or supporting someone.
JA: 旅行中、犬の面倒をみてくれない?
EN: Could you take care of my dog while I'm traveling?