If a^b = b^a, then what is \frac{\left(\frac{a}{b}\right)^{\frac{a}{b}}}{a^{\frac{a}{b}-1}} equal to?

Explanation

Given a^b = b^a, we know a = b^{a/b}. The expression simplifies to \frac{a^{a/b}}{b^{a/b}} \times a^{1 - a/b} = \frac{a}{b^{a/b}}. Substituting b^{a/b} = a, we get \frac{a}{a} = 1.

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