When exponents get funny

Algebra Level 5

\[\huge {\sqrt[4]{\sqrt[x]{4}}}^{\tfrac{1}{\sqrt[4]{{\left(\sqrt[x]{4x^4}\right)}^{x^4}}}} = 4^{4^{-17}x^{-x^3 - 1}}\]

Find the real value of \(x\) satisfying the real equation above.

\(\text{Note}\):- Here \(x \neq \{-1,0,1\}\).


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