Physics

The key is recognizing that uncertainty propagates through functions using logarithmic differentiation. Since $z$ involves products and powers, take the natural log of both sides to convert multiplication into addition—this lets you add fractional uncertainties linearly rather than dealing with messy derivatives. Once you have the fractional uncertainty in $z$, multiply by 100 to get the percentage.

The key is recognizing that uncertainty propagates through functions using logarithmic differentiation. Since $z$ involves products and powers, take the natural log of both sides to convert multiplication into addition—this lets you add fractional uncertainties linearly rather than dealing with messy derivatives. Once you have the fractional uncertainty in $z$, multiply by 100 to get the percentage.