Answer
$m^{\frac{1}{12}}$
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[4]{\sqrt[3]{m}}
.$
$\bf{\text{Solution Details:}}$
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[4]{m^{1/3}}
\\\\=
\left( m^{1/3} \right)^{1/4}
.\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}
m^{\frac{1}{3}\cdot\frac{1}{4}}
\\\\=
m^{\frac{1}{12}}
.\end{array}
