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Algebra Level 5

xxx+3×x2xx+2=aa(1a)/a \huge x^{x^{x+3}} \times x^{2x^{x+2}} = a^{a^{(1-a)/a}}

For all xx and aa real numbers that satisfy the equation above, and given that

xx×(1a)1a \Large x^{-x} \times \left( \frac1a\right)^{-\frac1a}

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

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