Монгол Бодлогын Сан

Заавар: $$\begin{gather*} x^{m}\cdot x^{n}=x^{m+n}\\ (x^m)^{n}=x^{mn}\\ \sqrt[m]{x^n}=x^{\frac{m}{n}} \end{gather*}$$

Бодолт: $$\begin{align*} \sqrt[4]{x^3\cdot\sqrt{x^{-4}\sqrt[3]{x^2}}}&=\big(x^3\cdot(x^{-4}\cdot x^{\frac23})^{\frac12}\big)^{\frac14}\\ &=\big(x^3\cdot(x^{-4+\frac23})^{\frac12}\big)^{\frac14}\\ &=\big(x^3\cdot (x^{-\frac{10}3})^{\frac12}\big)^{\frac14}\\ &=\big(x^3\cdot x^{{-\frac{5}3}}\big)^{\frac14}\\ &=\big(x^{3-\frac{5}3}\big)^{\frac14}\\ &=\big(x^{\frac{4}3}\big)^{\frac14}\\ &=x^{\frac13} \end{align*}$$