Answer
$\sqrt[12]{x^5}$
Work Step by Step
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 given expression is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt[3]{x^2}}{\sqrt[4]{x}}
\\\\=
\dfrac{x^{2/3}}{x^{1/4}}
.\end{array}
Using the Quotient Rule of the laws of exponents which states that $\dfrac{x^m}{x^n}=x^{m-n},$ the expression above simplifies to
\begin{array}{l}\require{cancel}
\dfrac{x^{2/3}}{x^{1/4}}
\\\\=
x^{\frac{2}{3}-\frac{1}{4}}
\\\\=
x^{\frac{8}{12}-\frac{3}{12}}
\\\\=
x^{\frac{5}{12}}
.\end{array}
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 given expression is equivalent to
\begin{array}{l}\require{cancel}
x^{\frac{5}{12}}
\\\\=
\sqrt[12]{x^5}
.\end{array}
