Paul's quotation is from the prophet Isaiah in the Old Testament. In the original passage, the word "I" refers to God and the word "you" is singular and refers to the Messiah. Here, Paul and Barnabas seem to be saying that the quotation also refers to their ministry.
Their rejection of the word of God is spoken of as if it were something they pushed away. AT: "Since you reject the word of God"
# consider yourselves unworthy of eternal life
"have shown that you are not worthy of eternal life" or "act as though you are not worthy of eternal life"
# we will turn to the Gentiles
Here "turn" refers to a change in to whom they would teach. AT: "we will now tell the message to the Gentiles"
# as a light
Here the truth about Jesus that Paul was preaching is spoken of as if it were a light that allowed people to see. (See: [[rc://en/ta/man/translate/figs-metonymy]])
# bring salvation to the uttermost parts of the earth
The abstract word "salvation" can be translated with the verb "to save." The phrase "uttermost parts" refers to everywhere. AT: "tell people everywhere in the world that I want to save them" (See: [[rc://en/ta/man/translate/figs-abstractnouns]])