[tex]Z:\\x > 0[/tex]
[tex]\frac{\sqrt[3]{x^{4}}\cdot\sqrt{x}}{x^{\frac{1}{3}}} = \frac{(x^{4})^{\frac{1}{3}}\cdot x^{\frac{1}{2}}}{x^{\frac{1}{3}}}=\frac{x^{4\cdot\frac{1}{3}}\cdot x^{\frac{1}{2}}}{x^{\frac{1}{3}}}=\frac{x^{\frac{4}{3}}\cdot x^{\frac{1}{2}}}{x^{\frac{1}{3}}}=\frac{x^{\frac{4}{3}+\frac{1}{2}}}{x^{\frac{1}{3}}} = \frac{x^{\frac{8}{6}+\frac{3}{6}}}{x^{\frac{2}{6}}} = \frac{x^{\frac{11}{6}}}{x^{\frac{2}{6}}} = x^{\frac{11-2}{6}} = \\\\=x^{\frac{9}{6}} = x^{\frac{3}{2}}=\sqrt{x^{3}} = \sqrt{x^{2}\cdot x} = x\sqrt{x}[/tex]
[tex]Lub\\\\\frac{\sqrt[3]{x^{4}}\cdot\sqrt{x}}{x^{\frac{1}{3}}}=\frac{\sqrt[3]{x^{4}}\cdot\sqrt{x}}{\sqrt[3]{x}} = \sqrt[3]{\frac{x^{4}}{x}}\cdot\sqrt{x} = \sqrt[3]{x^{3}}\cdot\sqrt{x} = x\sqrt{x}[/tex]
