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 \(b\).
by
Gabriel Benício