Answer
$\sqrt[12]{n}$
Work Step by Step
Using $x^{m/n}=\sqrt[n]{x^m}=\left(\sqrt[n]{x} \right)^m,$ then
\begin{array}{l}\require{cancel}
\sqrt[6]{\sqrt{n}}
\\\\=
\sqrt[6]{n^{1/2}}
\\\\=
\left( n^{1/2} \right)^{1/6}
.\end{array}
Using the Power Rule of the laws of exponents which is given by $\left( x^m \right)^p=x^{mp},$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
n^{\frac{1}{2}\cdot\frac{1}{6}}
\\\\=
n^{\frac{1}{12}}
.\end{array}
Using $x^{m/n}=\sqrt[n]{x^m}=\left(\sqrt[n]{x} \right)^m,$ then
\begin{array}{l}\require{cancel}
n^{\frac{1}{12}}
\\\\=
\sqrt[12]{n^1}
\\\\=
\sqrt[12]{n}
.\end{array}
