Numerical stability of computational results

Question

Let z be a function of a finite number of variables i.e. z=f(a,b,c,...). If we have the mathematical formula connecting z and the variables, we can determine how the value of z varies with a change in any of the input variables a,b,.... so on. It is clear that if in the formula some variable is raised to some high power (exponentiation), z will change steeply with respect to that variable. So numerical stability of z is less with respect to this particular variable because a small change (error) in this variable can lead to a large error in z. Viewed in this way, determinant of a matrix is a function of its elements. Many computations use determinant in the calculation as in Cramer's rule. So numerical stability is essentially dependent on the powers of the variables involved in the formula/relation. All the condition numbers, singular values etc are actually an index/summary of these powers. Is my understanding right? Or is there something more?