Now here we refer to the energy input being as a function of power and time. For voltage transformations, we assume that the transformation is instantaneous here.
So power input and power output are equal.
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Now the question asks to explain this. Explain questions require you to state a cause, note the effect and give a reason for it happening.
I would answer the question as follows:
Cause - Law of Conservation of Energy
Effect - Relationship can be derived relating to output and input voltages.
Reason - Go through explaining in words and equations using the conservation of energy and why this leads to input and output power are equal, etc.
Note at the end that the equation and explanation you derived applies to 100% efficient voltage transformations as energy transfers which aren't part of the voltage transformation (example heat losses) results in power losses.