Puzzles/Arithmetical puzzles/Two 4s Equal 64?/Solution

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Some answers are $\sqrt{\sqrt{\sqrt{4^{4!}}}}$, $\sqrt{\sqrt{{\sqrt{4}}^{4!}}}$, $4^{\log \sqrt{\sqrt{\sqrt{\exp 4!}}}}$ and $4^{-\lfloor \tan 4!\rfloor }$.