# 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 $$x \neq -1,0,1$$.

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