Possible Clues:

• Register with mirth a problematical mathematical aid
• Mathematics function
• Mathematical aid simplifying multiplication and division - a girl moth (anag)
• Slide rule's basis
• Record most of song on time with sovereign power
• Slide rule number
• Old-fashioned computing aid to record sound of a cadence
• Power to which base is raised
• Napier’s function, to record a beat, do we hear?
• Power left with Mao right after upheaval