Suppose we have the complex exponential $e^{jx}.$
I manipulate the exponential as follows:
$e^{jx} = (e^{j2\pi})^{\frac{x}{2\pi}} = 1^{\frac{x}{2\pi}} = 1.$
My question is if the power property in the first equation is valid.
Also if you can provide some additional information or theory about that it would be appreciated.
You can use the general rule $(a^m)^n=a^{m\times n}$ for real $a>0$ or when $m$ and $n$ are integers.
In other situations, it could lead to nonsense such as $-1=(-1)^1=((-1)^2)^{1/2}=1^{1/2}=1$.