Moses, whose prayer caused God to change His mind

God is unchanging or immutable.
His purpose has been fixed from eternity and He will establish it (Isa. 46:10; Eph. 1:11).
He does not change His mind as man does (1 Sam. 15:29).
So how do we explain the many Old Testament references to God repenting?
What kind of prayer does it take to get God, from our viewpoint, to "change His mind"?