Is it tedious?

Algebra Level 3

x=4(5+1)(54+1)(58+1)(516+1)\large x=\frac { 4 }{ \left( \sqrt { 5 } +1 \right) \left( \sqrt [ 4 ]{ 5 } +1 \right) \left( \sqrt [ 8 ]{ 5 } +1 \right) \left( \sqrt [ 16 ]{ 5 } +1 \right) }

Find (x+1)16\left( x+1 \right) ^{ 16 }.

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