$$$$
If
$$ {fuck}^{{fuck}^{fuck}}=\frac{1}{2}^{\sqrt{2}} $$
Rewriting right hand side
$$\equiv \frac{1}{2}^{\sqrt2\frac{\sqrt2}{\sqrt2}}$$
$$\equiv \frac{1}{2}^{2\frac{1}{\sqrt2}}$$
$$\equiv \frac{1^2}{2^2}^{\frac{1}{\sqrt2}}$$
$$\equiv \frac{1}{4}^{\frac{1}{\sqrt2}}$$
$$\equiv \frac{1}{4}^{\sqrt{\frac{1}{2}}}$$
$$\equiv \frac{1}{4}^{\frac{1}{2}^{\frac{1}{2}}}$$
$$\equiv \frac{1}{4}^{\frac{1}{4}^{\frac{1}{2}^{\frac{1}{2}}}}$$
$$\equiv \frac{1}{4}^{\frac{1}{4}^{\frac{1}{4}}}$$
$$\therefore fuck = \frac{1}{4}$$
