任せるよ。

to entrust (e.g. a task) to another; to leave to; to passively leave to someone else's facilities; to leave to take its natural course; to continue (something) in a natural fashion (without particular aim); to rely fully on one's (full strength, great ability, long time taken) to get something done

indicates certainty, emphasis, contempt, request, etc.; used when calling out to someone; used to catch one's breath or get someone's attention; yo!