To rewrite the logarithmic equation \( \log_2{16} = 4 \) as an exponential equation, we express it in the form \( b^y = x \), where \( b \) is the base, \( y \) is the exponent, and \( x \) is the result.
Therefore, the exponential form would be:
\[ 2^4 = 16 \]
So, the correct response from the options provided is:
\( 2^4 = 16 \)