Funny exponents

Algebra Level 4

\[\huge \sqrt[\large{\dfrac{1}{4x}}]{{\left(\sqrt[4x]{4^x}\right)}^{x^4}} = 4^{\left(\sqrt[4x]{{\left(\sqrt[4x^4]{x^4}\right)}^{x^4}}\right)}\]

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

The answer is of the form \(\dfrac{a}{b}\) where \(a\) and \(b\) are positive co-prime integers. Then find the value of \(a + b\).

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

This is one part of the set Fun with exponents

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