An algebra problem by Saurav Pal

Algebra Level 2

If

x=4(5+1)(54+1)(58+1)(516+1),x=\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)},

then what is the value of (1+x)48?(1+x)^{48}?

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