NO. Since "c" has no dimensions, the value of its exponent "n" is irrelevant to dimensional analysis, and thus dimension analysis cannot be used to determine the value of "n".
Dimensional analysis is not applicable to proportionality constants, trigonometrical or exponential equations, equation consisting of sum or difference of some quantities and equation consisting of more than three fundamental quantities.
What is Dimensional analysis?
What is a dimensional analysis used for?
Dimensional analysis is a method used in engineering and the physical sciences to reduce physical properties like acceleration, viscosity, and energy to their three basic dimensions of length, mass, and time (T).
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