Answer
$4$
Work Step by Step
We know that $\log_a {x^n}=n\cdot \log_a {x}$.
Hence,
$e^{\log_{e^2}{16}}=e^{\log_{e^2}{4^2}}=e^{2\log_{e^2}{4}}$.
We also know that $a^{\log_a {x}}=x$.
Thus,
$e^{2\log_{e^2}{4}}
\\=(e^2)^{\log_{e^2}{4}}
\\=4$
