Question Number 194316 by SajaRashki last updated on 03/Jul/23
$${if}\:\:{x}\in{R}\:\:\&\:\:{x}^{{x}^{\mathrm{6}} } =\left(\sqrt{\mathrm{2}}\right)^{\sqrt{\mathrm{2}}} \:\Rightarrow\:\:{x}=? \\ $$
Commented by Frix last updated on 03/Jul/23
$${x}=\mathrm{2}^{\frac{\mathrm{1}}{\mathrm{4}}} \\ $$$$\Rightarrow\:{x}^{\mathrm{6}} =\mathrm{2}\sqrt{\mathrm{2}} \\ $$$$\left(\mathrm{2}^{\frac{\mathrm{1}}{\mathrm{4}}} \right)^{\mathrm{2}\sqrt{\mathrm{2}}} =\mathrm{2}^{\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}} =\left(\sqrt{\mathrm{2}}\right)^{\sqrt{\mathrm{2}}} \\ $$