P1933 Math002

$$$$

If

$${fuck}^{{fuck}^{fuck}}={\frac{1}{2}}^{\sqrt{2}}$$

Rewriting right hand side 

$$\equiv {\frac{1}{2}}^{\sqrt{2}\frac{\sqrt{2}}{\sqrt{2}}}$$

$$\equiv {\frac{1}{2}}^{2\frac{1}{\sqrt{2}}}$$

$$\equiv {\frac{1^2}{2^2}}^{\frac{1}{\sqrt{2}}}$$

$$\equiv {\frac{1}{4}}^{\frac{1}{\sqrt{2}}}$$

$$\equiv {\frac{1}{4}}^{\sqrt{\frac{1}{2}}}$$

$$\equiv {\frac{1}{4}}^{{\frac{1}{2}}^{\frac{1}{2}}}$$

$$\equiv {\frac{1}{4}}^{{\frac{1}{4}}^{{\frac{1}{2}}^{\frac{1}{2}}}}$$

$$\equiv {\frac{1}{4}}^{{\frac{1}{4}}^{\frac{1}{4}}}$$

$$\therefore fuck=\frac{1}{4}$$