target:Let's think step by step. Factoring $729=3^6$ and combining the roots
$\frac{1}{2}\frac{1}{3}\frac{1}{2}=\frac{1}{12}$, we get that $\sqrt{\sqrt[3]{\sqrt{\frac{1}{729}}}}=\left(\frac{1}{3^6}\right)^{\frac{1}{12}}=\frac{1}{3^{\frac{1}{2}}}=\frac{3}{\sqrt{3}}$