Complex sentence: In the late 1970s, her best known show, The Sunday Request Show, began its run; originally broadcast on Sunday afternoons before moving to a slot immediately after the Top 40 in 1982.
Split into simpler sentences: In the late 1970s, her best known show--the Sunday request show-began its run. It was originally broadcast on Sunday afternoons, before moving to a slot immediately after the Top 40 in 1982.