If \( \lim _{x \rightarrow a} \frac{a^{x}-x^{a}}{x^{x}-a^{a}}=-1 \) and \( a0 \), then find the ...

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If \( \lim _{x \rightarrow a} \frac{a^{x}-x^{a}}{x^{x}-a^{a}}=-1 \) and \( a0 \), then find the value of \( a \).
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