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(B) If a physical quantity is raised to a power $n$ (i.e.,$x^n$),the relative error in the result is given by $n 	imes (\Delta x / x)$.As the exponen

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Because the relative error in a quantity with a large exponent is multiplied by the exponent,leading to a significant increase in the final relative error.

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(B) If a physical quantity is raised to a power $n$ (i.e.,$x^n$),the relative error in the result is given by $n 	imes (\Delta x / x)$.As the exponent $n$ increases,the relative error in the measurement is magnified by a factor of $n$.Therefore,even a small error in the initial measurement of $x$ can lead to a large error in the final result.To ensure the final result remains within acceptable limits of accuracy,the initial measurement of quantities with large exponents must be performed with very high precision.

Why should the measurement of physical quantities with large exponents in an experiment be taken with high precision?

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