Exegesis:
idou dedōka humin ‘behold, I have given you.’ idou (cf. on 1.20) has here the force of a confirmative particle. dedōka points to an act in the past which is still effective.
tēn exousian tou patein epanō opheōn kai skorpiōn ‘the authority to tread on snakes and scorpions,’ because of the article tēn referring to a specific authority. For exousia cf. on 4.6, 32. Here it is used in the sense of ‘effective authority,’ or, ‘power.’
pateō (also 21.24) here intransitive ‘to walk,’ ‘to tread,’ ‘to trample,’ in 21.24 transitive.
epanō ‘on,’ cf. on 4.39.
ophis (also 11.11) ‘snake,’ general term, but here of dangerous snakes.
Both ophis and skorpios (cf. also 11.11, 12), though here to be taken literally, symbolize harmful powers.
kai epi pasan tēn dunamin tou echthrou ‘and (authority) over all the power of the enemy,’ with exousian understood from tēn exousian. As compared with the preceding phrase this is of a general and non-symbolic nature. dunamis may have the connotation of ‘(armed) forces.’
ho echthros ‘the enemy’ refers here to the devil.
kai ouden humas ou mē adikēsē ‘and nothing will harm you,’ or ‘and he will not harm you in any respect,’ preferably the former rendering which has ouden as subject of adikēsē. ou mē is a strong negation, cf. on 1.15, and reinforces ouden … ou which, by itself, is already stronger than ouden alone.
adikeō ‘to harm,’ ‘to hurt.’
Translation:
I have given you authority to, preferably, ‘power to,’ or, with a syntactic shift, ‘I have empowered/enabled you to,’ ‘I have made you so strong that you can.’
Serpent, or, ‘poisonous snake,’ or the name of a common local species or equivalent.
Where the scorpion is unknown, the name of another dangerous reptile will do, e.g. that of a poisonous lizard (Medumba), or a centipede whose bite causes a swelling (East and Toraja-Sa’dan).
And over, or “and cope with” (The Four Gospels – a New Translation), ‘to subdue’ (Balinese, Toraja-Sa’dan). The head of the construction may have to be repeated, ‘and power over.’
The enemy. The referent may be suggested by marking the noun (for which see on 1.71) as a proper name (e.g. in Good News Translation, Bible de Jérusalem), or made explicit, cf. ‘the Evil-one’ (Tae’ 1933), ‘Satan’ (Tboli).
Hurt, or, ‘cause harm/pain/evil to,’ ‘make suffer’; or, ‘to do-something-to’ (a derivation of ‘why’ used in a clearly pejorative sense) (Tae,’ 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.