Find the relative error in Z, if `Z=A^(4)B^(1//3)//CD^(3//2)` and the percentage error in the measurements of A,B,C and D are 4%,2%,3% and 1% respectively.

Explanation

`(DeltaZ)/Z=4((DeltaA)/A)+1/3((DeltaB)/B)+(DeltaC)/C+3/2((DeltaD)/D)`
Given that `(DeltaA)/A xx 100 =4(DeltaB)/Bxx100=2, (DeltaC)/Cxx100=3` and `(DeltaD)/Dxx100`=1
`therefore (DeltaZ)/Zxx100(4xx4)+(1/3xx2)+3+(3/2xx1)`
`=1.6+2/3+3+3/2`=6.76%
The percentage error in the measurement of Z is 6.76%
Therefore, the relative error in Z is 0.0676