Arrow notation

Arrow Notation is a famous notation invented by Knuth in 1976 to represent large numbers.

Formula
$$a \uparrow b = a^b$$

$$a \uparrow\uparrow b = \underbrace{a \uparrow a \uparrow a \uparrow \ldots}_{b}$$

$$a \uparrow\uparrow\uparrow b = \underbrace{a \uparrow\uparrow a \uparrow\uparrow a \uparrow\uparrow \ldots}_{b}$$

$$a \uparrow\uparrow\uparrow\uparrow b = \underbrace{a \uparrow\uparrow\uparrow a \uparrow\uparrow\uparrow a \uparrow\uparrow\uparrow \ldots}_{b}$$

Examples
$$2 \uparrow 3 = 2^3 = 8$$

$$10 \uparrow 100 = 10^100 = googol$$

$$3 \uparrow\uparrow 4 = 3 \uparrow 3 \uparrow 3 \uparrow 3= 27 \uparrow 3 \uparrow 3 = 19683 \uparrow 3 = 762559748497$$

$$6 \uparrow\uparrow 6 = 6 \uparrow 6 \uparrow 6 = 46656 \uparrow 6 = 10314424798490535546171949056$$

$$2 \uparrow\uparrow\uparrow 2 = 2 \uparrow\uparrow 2 = 2 \uparrow 2 = 2^2 = 4$$

$$3 \uparrow\uparrow\uparrow 2 = 3 \uparrow\uparrow 2 = 3 \uparrow 3 = 3^2 = 9$$

2 \uparrow\uparrow\uparrow 3 = 2 \uparrow\uparrow 2 \uparrow\uparrow 2 = 4 \uparrow\uparrow 2 = 4 \uparrow 2 = 4^2 = 16