The right hand of the Lord is exalted (compare the parallel expression in Exodus 15:6, "Thy right hand, O God, is become glorious in power"). When God's right hand effects a deliverance, it gets, as it were, additional glory to itself.
The right hand of the Lord doeth valiantly. So, already, in Psalms 118:16. Repetition is a special characteristic of this psalm (see Psalms 118:1, Psalms 118:2, Psalms 118:3, Psalms 118:4; Psalms 118:8, Psalms 118:9; Psalms 118:10-12, etc.
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