User:Upquark/sandbox

$${^{n}a} = {a^{a^{\cdot^{\cdot^{a}}}}}$$

$${2^4} = 2 \times 2 \times 2 \times 2 = 16$$

$${^{4}2} = {2^{2^{2^2}}} = {2^{2^4}} = {2^{16}} = 65536$$

$${3^4} = 3 \times 3 \times 3 \times 3 = 81$$

$${^{4}3} = {3^{3^{3^3}}} = {3^{3^{27}}} = {3^{7625597484987}} \approx {10^{3638334640024}}$$

$$3 \uparrow 2 = {3^2}$$

$$3 \uparrow\uparrow 2 = {^{2}3} = {3^{3^3}}$$

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

$$\frac{^{2}5}{^{3}2}$$ $$\frac{^{4}2}{^{2}3}$$