Answer
$\sqrt[6]{x^5}$
Work Step by Step
Using $a^{-x}=\dfrac{1}{a^x}$ or $\dfrac{1}{a^{-x}}=a^x,$ then
\begin{array}{l}\require{cancel}
\sqrt{x\sqrt[3]{x^2}}
\\\\=
\sqrt{x\cdot x^{2/3}}
\\\\=
(x\cdot x^{2/3})^{1/2}
.\end{array}
Using the Product Rule of the laws of exponents which is given by $x^m\cdot x^n=x^{m+n},$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
(x\cdot x^{2/3})^{1/2}
\\\\=
\left( x^{1+\frac{2}{3}} \right)^{1/2}
\\\\=
\left( x^{\frac{3}{3}+\frac{2}{3}} \right)^{1/2}
\\\\=
\left( x^{\frac{5}{3}} \right)^{1/2}
.\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}
\left( x^{\frac{5}{3}} \right)^{1/2}
\\\\=
x^{\frac{5}{3}\cdot\frac{1}{2}}
\\\\=
x^{\frac{5}{6}}
.\end{array}
Using $x^{m/n}=\sqrt[n]{x^m}=\left(\sqrt[n]{x} \right)^m,$ then
\begin{array}{l}\require{cancel}
x^{\frac{5}{6}}
\\\\=
\sqrt[6]{x^5}
.\end{array}
