# I Error propagation of exponentials

1. Mar 19, 2016

I am just wondering why there is a discrepancy between two different methods for error propagation. For example, if you have $Q = (a)(b)(c)$ then the relative error in Q is simply the square root of the sum of the squares of each of the terms being multiplied together, correct? But what if $Q = (a)(a)(a)$. Why isn't the relative error in Q now simply once again the square root of the sum of the squares of a (which in this case would be 3 terms)? I understand the derivation for the relative error in $Q = a^3$ being $3 \frac {\Delta a}{a}$ but just don't quite understand why the earlier rule pertaining to basic multiplication and division no longer applies. What is the reason for a discrepancy between the two methods of error propagation? Can't exponentiation (using positive integers) be considered as just an extension of multiplication?

2. Mar 19, 2016

### Knower

Notice that in Q = (a)(b)(c) the terms a, b and c are considered to be independent in the sense that the error of one of them is independent from the error to another. But if a = b = c then the "three" terms are not independent.

3. Mar 20, 2016