Digits and Powers

Algebra Level 3

$\LARGE \left(\sqrt[1,000,000]{\left(\sqrt[10,000]{\left(\sqrt[100]{10^{10}}\right)^{1,000}}\right)^{100,000}}\right)^{10,000,000}$

How many digits does the number above have when written in decimal representation?

10,001 10,000 1,001 1,000 100,000 99,999