The expression $e^{\ln{x}}$ simplifies to just $x$.

Here's why:

• The natural logarithm function $\ln{x}$ is the inverse of the exponential function $e^x$.
• This means $e^{\ln{x}} = x$ for any positive $x$.

Thus, the simplified expression is:

$e^{\ln{x}} = x$

Would you like a more detailed explanation, or have any questions?

Here are some related questions to expand your understanding:

1. What is the inverse function of $\ln{x}$?
2. How does the property of logarithmic and exponential functions relate to solving equations?
3. What is $e^{\ln{(x^2)}}$ and how does it simplify?
4. How do logarithms with different bases affect the simplification process?
5. Can $e^{\ln{x}}$ simplify if $x$ is negative?

Tip: Remember, the logarithmic and exponential functions are inverses, which makes simplifications involving $e^{\ln{x}}$ straightforward!