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 $4^{-\lfloor \tan {4!}\rfloor }$.