2. Compute the positive real number $x$ satisfying
$$
x^{\left(2 x^{6}\right)}=3 .
$$
Answer:
$$
\sqrt[6]{3}
$$

Let $t=x^{6}$, so $x^{2 t}=3$. Taking this to the third power gives $x^{6 t}=27$, or equivalently $t^{t}=3^{3}$. We can see by inspection that $t=3$, and this is the only solution as for $t>1$, the function $t^{t}$ is monotonically increasing, and if $0<t<1, t^{t}<1$. Solving for $x$ gives $x^{6}=3$, or $x=\sqrt[6]{3}$.