Pentation is the 5th hyperoperation, and the first one is addition. Pentation is just repeated tetration, but it produces extremely large unimaginable numbers, a simple 2 ↑↑↑ 3 (or often displayed as 32) is equal to 65,536. Another example is 3 ↑↑↑ 2. It is equal to 7,625,597,484,987 (~7.625 trillion).
Pentation is calculated like this: 2 ↑↑↑ 3 = 2²2 = ⁴2 = 2^2^2^2 = 65,536
Using 2 pentated to 4 as an example, 2 pentated to 4 is equal to 2 tetrated to 2 repeating 4 times, which can be written with Knuth's up-arrow notation like below.
2↑↑↑4 = 2↑↑2↑↑2↑↑2
From this point, each tetration can be evaluated individually, starting from the ends.
2↑↑2 = 2^2, which is equal to 4. Then, 2↑↑4 = 2^2^2^2
2^2^2^2 = 2^2^4 = 2^16 = 65536
Finally, we have 2 ↑↑65536, or 2 tetrated to 65536. This is a power tower of 2s with 65536 twos (Including the base), written as 2^2^2…^2^2
This value is far too large to give be written conventionally, even with scientific notation, and as an example, the value of 2↑↑↑4 is larger than the number of atoms in the observable universe to the power of itself, around 10^(8x10^81)
(Hyperoperations often cannot be evaluated how we usually would, so they are kept in the form of whatever hyperoperation notation is used most of the time)
The word "Pentation" was coined by Reuben Goodstein (An English Mathematician) by joining together penta- (which is the suffix for five) and iteration (A mathematical function). It was how he usually named hyperoperations.