$\lim\limits_{x\to 0}\bigg[\large\frac{1^x+2^x+3^x+.........n^x}{n}\bigg]^{\Large\frac{1}{x}}$ is

$\begin{array}{1 1}(a)\;(n!)^n&(b)\;(n!)^{\large 1/n}\\(c)\;n!&(d)\;\log_e( n!)\end{array}$