Answer
$\sqrt[24]{x^{23}}$
Work Step by Step
Using $a^{m/n}=\sqrt[n]{a^m}$ and the laws of exponents, then,
\begin{array}{l}
\sqrt[3]{x}\cdot\sqrt[4]{x}\cdot\sqrt[8]{x^3}
\\\\=
x^{1/3}\cdot x^{1/4}\cdot x^{3/8}
\\\\=
x^{\frac{1}{3}+\frac{1}{4}+\frac{3}{8}}
\\\\=
x^{\frac{8}{24}+\frac{6}{24}+\frac{9}{24}}
\\\\=
x^{\frac{23}{24}}
\\\\=
\sqrt[24]{x^{23}}
.\end{array}
