If you are unaware of exponents and the notation:
For whole numbers a and b, then exponents are written ab or a^b, and read "a raised to the power of b", "a to the power of b", "a to the b", or similar.
a^b is equal to a×a×...×a with b a's.
Note that a^b and b^a is not always equal. For example, 2^3 = 2×2×2 = 8, but 3^2 = 3×3 = 9.
When the exponents are stacked, such as abc or a^b^c, it is a general consensus that the exponents are calculated from top to bottom, or right to left.
2^3^4 = 2^(3^4) = 2^81 = 2.4178516392292583e+24
(2^3)^4 = 8^4 = 4096
Revisit the definitions of multiplication and exponentiation:
\(\begin{align}a\times b&=\underset{b\;a\text{'s}}{\underbrace{a+a+\cdots+a}}\\a\text{^}b&=\underset{b\;a\text{'s}}{\underbrace{a\times a\times\cdots\times a}}\end{align}\)
We can see to extend the series of operation, which tetration achieves:
\(a\uparrow\uparrow b=\underset{b\;a\text{'s}}{\underbrace{a\text{^}a\text{^}\cdots\text{^}a}}\)
Tetration is also written as a^^b.
Remember that the exponents are solved from top.
3^^3 = 3^3^3 = 3^(3^3) = 3^27 = 7625597484987
After tetration, the series can be extended such as pentation:
\(a\uparrow\uparrow\uparrow b=\underset{b\;a\text{'s}}{\underbrace{a\uparrow\uparrow a\uparrow\uparrow\cdots\uparrow\uparrow a}}\)
The repeated tetrations are solved from right to left as exponents.
The number of arrows are increased as the operation become powerful. n arrows are often abbreviated as ↑n or {n}.
In general, \(a\uparrow^{c+1}b=\underset{b\;a\text{'s}}{\underbrace{a\uparrow^ca\uparrow^c\cdots\uparrow^ca}}\)
Sometimes, you find yourself over welmed by stuff like 10^^^10^^^10^^^10^^10^^10^10^10^328. OmegaNum.js condenses this by counting the number of repeated operations.
If we have 10{n} repeated m times, it is condensed into (10{n})m or (10{n})^m. These are finally chained back into a number.
The number above can be condensed into (10^^^)^3 (10^^)^2 (10^)^3 328.