Answer
$100^x$ grows slower than $x^x$.
Work Step by Step
We will find the limit $\lim_{x\to\infty}\frac{100^x}{x^x}.$
1) If it is equal to zero then $100^x$ grows slower than $x^x$;
2) If it is equal to $\infty$ then $100^x$ grows faster than $x^x$;
3) If it is equal to some non zero constant then their growth rates are comparable.
$$\lim_{x\to\infty}\frac{100^x}{x^x}=\lim_{x\to\infty}\left(\frac{100}{x}\right)^x=\left[\left(\frac{100}{\infty}\right)^\infty\right]=\left[0^\infty\right]=0,$$
and thus $100^x$ grows slower than $x^x$.
