9 The three aorist participles νηστεύσαντες (nēsteusantes), προσευξάμενοι (proseuxamenoi), and ἐπιθέντες (epithentes) are translated as temporal participles. Although they could indicate contemporaneous time when used with an aorist main verb, logically here they are antecedent. On fasting and prayer, see Matt 6:5, 16; Luke 2:37; 5:33; Acts 14:23.
10 Normally English style, which uses a coordinating conjunction between only the last two elements of a series of three or more, would call for omission of “and” here. However, since the terms “fasting and prayer” are something of a unit, often linked together, the conjunction has been retained here.
11 The placing of hands on Barnabas and Saul (traditionally known as “the laying on of hands”) refers to an act picturing the commission of God and the church for the task at hand.

In other versions

Then after fasting and praying they laid their hands on them and sent them off.

So after they had fasted and prayed, they placed their hands on them and sent them off.

Then after they had fasted, prayed, and laid hands on them, they sent them off.

So after more fasting and prayer, the men laid their hands on them and sent them on their way.

Then, after they had fasted and prayed and placed their hands on them, they sent them away.

And when they had fasted and prayed, and laid their hands on them, they sent them away.

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