Suppose ∑ni=1 bi xi = Z; we multiply the numerator and denominator by exp(z) toobtain Equation (2)

To rewrite the equation by multiplying the numerator and the denominator by $\exp(Z)$, we can go through the following steps:

1. Identify the Original Expression: The original expression given is: $\sum_{i=1}^{n} b_i x_i = Z$

2. Multiply Numerator and Denominator by $\exp(Z)$: We want to multiply both sides of the equation by $\exp(Z)$. For a fraction, this would generally look like: $\frac{\sum_{i=1}^{n} b_i x_i}{1} \cdot \frac{\exp(Z)}{\exp(Z)} = Z \cdot \frac{\exp(Z)}{\exp(Z)}$ which simplifies to: $\frac{\exp(Z) \sum_{i=1}^{n} b_i x_i}{\exp(Z)}$

3. Simplify: Since $Z = \sum_{i=1}^{n} b_i x_i$, we can replace $Z$ back in the equation: $\frac{\exp(Z) Z}{\exp(Z)} = Z$

4. Conclusion: Thus, the equation transforms accordingly but retains its value.

Final Answer

The modified equation becomes: $\frac{\exp(Z) \sum_{i=1}^{n} b_i x_i}{\exp(Z)} = Z$