For z = a ^ 2 x ^ 3 y(1)/(2) , where ' a ' is a constant. If...

Given: $z = {a}^{2}{x}^{3}y\dfrac{1}{2}$

Relative error is given by

$\dfrac{∆ z}{z} = \left[3 \times \dfrac{∆ x}{x} + \dfrac{1}{2} \times \dfrac{∆ y}{y}\right]$

Now, maximum percentage error in $z$ is

$\dfrac{∆ z}{z} \times 100 = \left[3\left(4\right) + \dfrac{1}{2}\left(2\right)\right] \times 100$

$= 18$.