If Z = A ^ 2 B ^ 3 C ^ 4 , then the relative error in Z will be

Given: $Z = \dfrac{{A}^{2}{B}^{3}}{{C}^{4}}$

When quantities are multiplied or divided, the relative error in the result is the sum of the relative errors in the multipliers.

So, $\dfrac{∆ Z}{Z} = \left[\dfrac{∆ A}{A} + \dfrac{∆ A}{A} + \dfrac{∆ B}{B} + \dfrac{∆ B}{B} + \dfrac{∆ B}{B} + \dfrac{∆ C}{C} + \dfrac{∆ C}{C} + \dfrac{∆ C}{C} + \dfrac{∆ C}{C}\right]$

Thus, relative error is

$\dfrac{∆ Z}{Z} = \left[2 \times \dfrac{∆ A}{A} + 3 \times \dfrac{∆ B}{B} + 4 \times \dfrac{∆ C}{C}\right]$