Yay for 2014! #2

Algebra Level 4

Given that

\[ 2014^{2} = 4056196 \]

find the sum of the digits of the exact value of

\[ (20142014.2014)^{2} \]

Notes:

Exact value means that no rounding occurs while calculating, so the exact value of \( (2.1)^{2} \) is \(4.41\), not \(4.4\) or \(4\).

The sum of the digits of a number includes the digits of any decimal places, so the sum of the digits of \(4.41\) would be \(4 + 4 + 1 = 9\).

This problem is part of the set Yay for 2014!.

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