For $a=\dfrac1{16}$, consider the (finite) power tower,

$\Large x_n=\underbrace{a^{a^{\cdot^{\cdot^{a^a}}}}}_{2n \; a\text{'s}}$

For example, $x_1=a^a$ and $x_2=a^{a^{a^a}}$.

Find $\displaystyle \lim_{n\to\infty}x_n$, to three significant figures.

**Bonus** What happens if we consider a power tower with an **odd** number of $a$'s?

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