# Simplify the Expression

## 28 October 2013

This sequence interests me chiefly because at first glance it looks wrong. $e^{\ln^2 x}$ should expand to $\left(e^{\ln x}\right)^{2}$, should it not? Only, it doesn’t because of the algebraic properties of exponents.

Given such context, it makes more sense and becomes more obvious why the original simplifies the way it does.

I restrict $x$ and $y$ to $\mathbb{R}$ because I haven’t yet investigated whether the properties hold for the imaginary numbers.