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

Given: $Z=\frac{A^2{B}^3}{C^4}$

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

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

Thus, relative error is 

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