Luke 10:19

And over all the power of the enemy

(κα επ πασαν την δυναμιν του εχθρου). This is the heart of "the authority" (την εξουσιαν) here given by Jesus which is far beyond their expectations. The victory over demons was one phase of it. The power to tread upon serpents is repeated in Mark 16:18 (the Appendix) and exemplified in Paul's case in Malta (Acts 28:3-5). But protection from physical harm is not the main point in this struggle with Satan "the enemy" (Matthew 13:25; Romans 16:20; 1 Peter 5:8).Nothing shall in any wise hurt you

(ουδεν υμας ου μη αδικησε). Text has future active indicative, while some MSS. read αδικηση, aorist active subjunctive of αδικεω, common verb from αδικος (α privative and δικος), to suffer wrong, to do wrong. The triple negative here is very strong. Certainly Jesus does not mean this promise to create presumption or foolhardiness for he repelled the enemy's suggestion on the pinnacle of the temple.