Equations and Functions #2

Calculus Level 3

There are two distinct real numbers, \(a\) and \(b\). For every real number \(c\) that is equal to neither \(a\) nor \(b\), they satisfy:

\[\large \frac{c^2e^{c-a}}{b^2}\neq e^{b-a}=\frac{a^2}{b^2}\]

Given that \(b\neq0\), find the value of \(\dfrac{(abe)^4}{e^{ab}}\).


Notation: \(e\) is the Euler's number.

This problem is an advanced form of the problem <Equations and Functions #1>.

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