To entrust or leave a matter, task, or decision to someone else.
この件は山田さんに任せてください。
Please leave this matter to Mr. Yamada.
試験の準備は友達に一部を任せた。
I left part of the exam preparation to a friend.
社長は全体の方針決定を副社長に任せた。
The president entrusted the overall policy decisions to the vice president.
To leave something to chance or to let it take its own course; to allow something to happen without intervening.
細かいことは気にせず、成り行きに任せよう。
Don't worry about the details; let's leave it to chance.
あとは運に任せるしかない。
There's nothing left to do but leave it to luck.
To make free use of something (money, time, energy) or to give oneself over to something; often appears in the phrase '〜に任せて'.
彼は休日を趣味に任せて過ごした。
He spent his day off indulging in his hobbies.
感情に任せて言葉を発してはいけない。
You mustn't speak impulsively under the sway of your emotions.