Which is bigger: a googolplex or $10^{100!}$ A googol is defined as $ 10^{100}$
Let x = $10^{100}$
A googolplex is defined as $10^{x}$
Which is bigger: a googolplex or $10^{100!}$
I only know that:
$100! = 1×2×3×...×98×99×100$
$10^{100} = 10×10×10×...×10×10×10$
I think its easier to approach if I only compare the exponents, because they both have the same base $10$ anyways, but I don't know how to show which is bigger from $100!$ and $10^{100}$

The question boils down to whether $10^{100}$ is greater than $100!$ (same bases). But by Stirling's approximation,
$$100!\approx\sqrt{200\pi}(100/e)^{100}$$
and $100/e>33>10$ and $\sqrt{200\pi}<30$ so $100!>10^{100}$. Hence $10^{100!}$ is the bigger number.
