Complex sentence: Sam & Dave reunited in August 1971 and performed throughout most of the 1970s through 1981, and enjoyed a brief resurgence in popularity due to The Blues Brothers's 1979 recording of "Soul Man".
Split into simpler sentences: Sam & Dave reunited in August 1971 and performed throughout most of the decade through 1981. They enjoyed a brief resurgence in popularity due to the Blues Brothers's 1979 recording of "Soul Man".