This chapter answers parts from Section A of thePrimary Syllabus, even though study power is not specifically mentioned in any of the "abilities" there. This topic was examined in Question 19 from the second paper of 2011. It is revisited in the Required Reading chapter for the Part II exam ("Study power, population and sample size"); in the Fellowship Exam Question 23 from the second paper of 2008 and Question 25 from the first paper of 2006 both asked the candidates to define "study power".
In summary, the commonest reason for a negative result is a small sample size. You need a sufficiently large sample to detect a given size of effect. The large the sample, the more likely you are to detect a true treatment effect. The point of calculating power is that you can use it to calculate a sufficient sample size, and not run the risk of performing a pointless negative study (thus exposing patients to risk), nor performing a pointlessly expensive study (collecting data from an unnecessarily large group of patients)
Power nearly always depends on the following three factors: