Cunning exponents

Algebra Level 3

$\large {\sqrt{x}}^{\sqrt[4]{x}} = \sqrt[x]{\sqrt[4]{x}}$

Find the real value of $x$ which satisfies the above equation.

The answer in the simplest form is of the form $\dfrac{1}{\sqrt[5]{a}}$, then find the value of $a$.

Note:- Here $x \neq 1$

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