Crazy exponents

Algebra Level 4

\[\Large {\left({\left(\sqrt{x}\right)}^{4\sqrt{4x^{16}}}\right)}^{\sqrt[4]{16x^8}} = {\left({\left(x^{4x^2}\right)}^{\sqrt[8]{4x^8}}\right)}^{16\sqrt{\sqrt{x}}}\]

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

The answer is of the form \(\sqrt[27]{a}\), then submit the value of \(a\)

Here \(x \neq 0,1\)


This is one part of the set Fun with exponents
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