Exegesis:

eipon hēmin ‘tell us,’ imperative, either modifying indirect questions (cf. punctuation of GOOD NEWS BIBLE), or introducing direct questions (cf. punctuation of Nestle), preferably the latter.

en poia exousia ‘by what authority.’ poios, lit. ‘of what kind?,’ may be equivalent to tis and mean ‘what?,’ or take the place of the genitive of interrogative tis and mean ‘whose?’ Here the former is preferable. For exousia cf. on 4.6, 32.

tauta poieis ‘are you doing these things.’ tauta may either refer to Jesus’ behaviour generally (cf. An American Translation, Phillips) or to his teaching and preaching specifically, probably the latter.

ē tis estin ho dous soi tēn exousian tautēn ‘or who it is who gave you this authority?’ ē introduces a second question, which refers to the origin of Jesus’ authority.

Translation:

By what authority you do these things, or ‘what (sort of) authority/right you have (or, you received) to do this, or, to do what you are doing here,’ ‘what authority you-have-as-authority to do these things’ (Toraja-Sa’dan), ‘what authority you rely-on to do these-your-deeds’ (Batak Toba).

Quoted with permission from Reiling, J. and Swellengrebel, J.L. A Handbook on the Gospel of Luke. (UBS Handbook Series). New York: UBS, 1971. For this and other handbooks for translators see here . Make sure to also consult the Handbook on the Gospel of Mark for parallel or similar verses.