# Dedication pays off!

Algebra Level 5

$\huge x^{x^{x+3}} \times x^{2x^{x+2}} = a^{a^{(1-a)/a}}$

For all $$x$$ and $$a$$ real numbers that satisfy the equation above, and given that

$\Large x^{-x} \times \left( \frac1a\right)^{-\frac1a}$

can be expressed as $$\displaystyle x^b$$, where $$b$$ is an integer, find the value of $$b$$.

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