For a quantity $X = \frac{A^p B^q}{C^r D^s}$, the maximum percentage error in $X$ is given by: $\%E_X = p(\%E_A) + q(\%E_B) + r(\%E_C) + s(\%E_D)$

In the given equation, $X = A^2 B^3 C^{-1} D^{-1/2}$. Note that the powers are always taken as positive when summing errors. $\%E_X = 2(\%E_A) + 3(\%E_B) + 1(\%E_C) + \frac{1}{2}(\%E_D)$

Given percentage errors:

• $\%E_A = 1\%$
• $\%E_B = 2\%$
• $\%E_C = 3\%$
• $\%E_D = 4\%$

Substitute these values into the formula: $\%E_X = 2(1\%) + 3(2\%) + 1(3\%) + \frac{1}{2}(4\%)$ $\%E_X = 2\% + 6\% + 3\% + 2\%$ $\%E_X = 13\%$