The value of \( \lim _{x \rightarrow 0}\left(\frac{1^{x}+2^{x}+3^{x}+\ldots+n^{x}}{n}\right)^{a ...

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The value of \( \lim _{x \rightarrow 0}\left(\frac{1^{x}+2^{x}+3^{x}+\ldots+n^{x}}{n}\right)^{a / x} \) is
(a) \( (n !)^{8 / n} \)
(b) \( n ! \)
(c) \( a^{n !} \)
(d) Doesn't exist
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