ExpantaNum.js

A large number library reaching {10,9e15,1,2} in Bower's operator notation.
For the code, you can find it here, and you can clone, or copy and paste it, or install via npm to use it.
For smaller numbers, use other libraries such as:

How it works

This library works by storing the sign, layer, and an array.
The sign is either 1 or -1, positive or negative respectively.
Array holds small part of the magnitude; Array [[a0,b0],[a1,b1],[a2,b2],[a3,b3],...] represents:

The layer is the large part of the magnitude. Together with array, it represents Jlayer [value represented by array], where Jx=10{x}10. Learn what it means
Therefore, array [[0,23.2352],[1,2],[2,6],[3,0],[4,1],[5,4]] represents (10↑5)410↑4(10↑↑)6(10↑)223.2352, which without parenthesis becomes 10↑510↑510↑510↑510↑410↑↑10↑↑10↑↑10↑↑10↑↑10↑↑10↑10↑23.2352. Using LaTeX, I can sort of expands into decimal. To reduce lag, I will put the source code here. You can copy them in somewhere to see.

Yeah, that's enormous.

Document

You can find the full document here.

Known bugs

Test here

String or Array to big number

Output here

Arbitrary code execution();
Output(eval()) here