Can Dimensional Analysis Determine the Exponent N in y=c^nat^2?

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Dimensional analysis cannot determine the integer value of the exponent N in the equation y=c^nat^2 because c is dimensionless, making c^n also dimensionless regardless of the value of n. The dimensions of Y, A, and T are known, but since C has no dimensions, it does not contribute to determining N. The conclusion is that dimensional analysis is ineffective in this case. The discussion raises a question about the nature of the problem, suggesting it may be related to homework. Ultimately, the inability to derive N through dimensional analysis is emphasized.
Dmt669
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In the equation y=c^nat^2, in other words... Y equals C to the N power times A times T to the second power, you wish to determine the integer value (1,2,etc.) of the exponent N. The dimensions of Y,A,and T are known. It is also known that C has no dimensions. Can dimensional analysis be used to determine N. Account for your answers, THANKS
 
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No. If c is dimensionless, then so is c^n, no matter what n is.
 
Is this homework ??
 

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