Crazy exponents

Algebra Level 5

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

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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