Answer
$k^{\frac{1}{6}}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the definition of rational exponents and the laws of exponents to simplify the given expression, $
\sqrt[3]{\sqrt[]{k}}
.$
$\bf{\text{Solution Details:}}$
Using the definition of rational exponents which is given by $a^{\frac{m}{n}}=\sqrt[n]{a^m}=\left(\sqrt[n]{a}\right)^m,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\sqrt[3]{\sqrt[2]{k}}
\\\\=
\sqrt[3]{k^{1/2}}
\\\\=
\left( k^{1/2} \right)^{1/3}
.\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}
k^{\frac{1}{2}\cdot\frac{1}{3}}
\\\\=
k^{\frac{1}{6}}
.\end{array}