Some Property!

$\Large{\begin{aligned} \sqrt[3]{x\sqrt{x}}&=(x\cdot x^{1/2})^{1/3}\\&=(x^{1+1/2})^{1/3}\\&=(x^{\color{#D61F06}{3}/2})^{1/\color{#D61F06}{3}}\\&=x^{1/2}=\sqrt x\end{aligned}}$ Make sure you know some Exponent Rules .

Relevant wiki: Rules of Exponents - Algebraic

$\large \sqrt[3]{x\sqrt{x}}$

Simplifying the expression,

$\large = \ \sqrt[3]{\sqrt{x^3}}$

Using the the rule of exponents,

$\large = \ \sqrt[6]{x^3}$

Thus,

$\large = \ x^{\frac{3}{6}}$

$\large = \ x^{\frac{1}{2}}$