How Do You Calculate Percentage Error in Z When Z is a Function of A and B?

[kd001]

Homework Statement

The quantity Z is a function of 2 variables A and B.
Z=A^4/B
A=1.253 (error0.005) B=20.7 (error 0.2)
Calculate percentage error in Z.

Homework Equations

I have the relevant error expressions
if Z=A/B (errorZ/Z)^2 = (errorA/A)^2 + (errorB/B)^2

if Z=A^n errorZ/Z=n.errorA/A

The Attempt at a Solution

I don't know how to combine the different standard error expressions.

Thanks for any help.

 

[Donaldos]

$$Z=\frac{A^4}{B}$$

$$Z=\frac A B \Rightarrow \frac{\Delta Z}{Z}=\frac{\Delta A}{A}+\frac{\Delta B}{B}$$

so in this case

$$\frac{\Delta Z}{Z}=\frac{\Delta \left(A^4\right)}{A^4}+\frac{\Delta B}{B}$$

and since

$$Z= A^n \Rightarrow \frac{\Delta Z}{Z}=n\frac{\Delta A}{A}$$

we have

$$\frac{\Delta \left(A^4\right)}{A^4}=4\frac{\Delta A}{A}$$