Almost AIME

Algebra Level 2

4(5+1)(54+1)(58+1)(516+1)\large \frac{4}{\big(\sqrt{5} + 1\big)\big(\sqrt[4]{5} + 1\big)\big(\sqrt[8]{5} + 1\big)\big(\sqrt[16]{5} + 1\big)}

If the above expression is equal to xx, find the value of (x+1)64 (x+1)^{64} .

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