[tex] \\x\sqrt{x\sqrt[3]{x\sqrt[4]{x^3\cdot\sqrt[3]{x}}}}=\\ x\sqrt{x\sqrt[3]{x\sqrt[4]{x^3\cdot x^{\frac{1}{3}}}}}=\\ x\sqrt{x\sqrt[3]{x\sqrt[4]{x^{\frac{10}{3}}}}}=\\ x\sqrt{x\sqrt[3]{x\cdot x^{\frac{10}{12}}}}=\\ x\sqrt{x\sqrt[3]{x^{\frac{22}{12}}}}=\\ x\sqrt{x\cdot x^{\frac{22}{36}}}=\\ x\sqrt{x^{\frac{58}{36}}}=\\ x\cdot x^{\frac{58}{72}}=\\ x^{\frac{130}{72}}=\\ x^{\frac{65}{36}} [/tex]
