Here "us" refers to the people of Israel that were living in Egypt. The speaker includes himself as one of the people whether he lived in Egypt or not. (See: [[rc://en/ta/man/translate/figs-exclusive]])
Here "a mighty hand" and "an outstretched arm" are metaphors for Yahweh's power. See how you translated these words in [Deuteronomy 4:34](../04/34.md). Alternate translation: "by showing his mighty power" (See: [[rc://en/ta/man/translate/figs-metaphor]])