For $z = a^2 x^3 y^{\frac{1}{2}}$, where '$a$' is a constant. If percentage error in measurement of '$x$' and '$y$' are $4\%$ and $12\%$, respectively, then the percentage error for '$z$' will be $\_\_\_\_$ $\%$.
For $z = a^2 x^3 y^{\frac{1}{2}}$, where '$a$' is a constant. If percentage error in measurement of '$x$' and '$y$' are $4\%$ and $12\%$, respectively, then the percentage error for '$z$' will be $\_\_\_\_$ $\%$.