$\sqrt[4]{x \sqrt[3]{x \sqrt{x}}} = \sqrt[8]{8}$ $x^{\frac{1}{24}}\times x^{\frac{1}{12}}\times x^{\frac{1}{4}}=2^{\frac{3}{8}}$ $x^{\frac{1}{24}+\frac{1}{12}+\frac{1}{4}}=2^{\frac{3}{8}} \to x^{\frac{9}{24}}=x^{\frac{3}{8}}=2^{\frac{3}{8}} \to x=2$