Simplify $\lim_{n \to +\infty}\left(1 + \frac{1}{n}\right)^{nx}=e^x$ I am trying to simplify this limit $\lim_{n \to +\infty}\left(1 + \frac{1}{n}\right)^{nx}=e^x$ into the well-known definition of $e^x$ as:
$$\lim_{n \to +\infty}\left(1 + \frac{1}{n}\right)^{nx}=e^x \iff \lim_{n \to +\infty}\left(1 + \frac{x}{n}\right)^{n}=e^x$$
I would prefer a clear explanation on how to transform the first expression into the second one without involving any other exponential limit definitions or logarithmic expressions, just using limits rules and algebra, and binomal expansion if necessary.
Thank you.

Hint: add pharenthesis to the expression, remember that according to power's rule, $a^{mn}=({a^m})^n$
