Maths on a Mug #3

This is one of my favourite puzzles. It is a simple, life long game. Using exactly four 4s make as many numbers as you can. You can use the operators \(+,\,-,\,\times,\,\div,\,!,\,\mbox{^},\,.,\,\sqrt{},\Gamma\) and concatenation. You must use all four 4s. Let me start you off with a couple:

\(\begin{align*}
0 &= 44 – 44, \\
1 &= \frac{44}{44}, \\
2 &= \frac{4}{4} + \frac{4}{4}.
\end{align*}\)

The value on the mug is a solution for the number 169.

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