Монгол Бодлогын Сан

Заавар: $\sqrt[n]{a^m}=a^{\frac{m}{n}}$ ба зэргийн чанар ашиглан бод.

Бодолт: $$\begin{align*} \text{Илэрх.}&=\left(\sqrt[4]{32\cdot\sqrt[3]{4}}+\sqrt[4]{64\sqrt[3]{\dfrac12}}-3\sqrt[3]{2\sqrt[4]2}\right)\cdot\dfrac3{\sqrt[12]{2^5}}\\ &=\left\{(2^5\cdot 2^{\frac23})^{\frac14}+(2^6\cdot(2^{-\frac13}))^{\frac14}-3\cdot(2\cdot2^{\frac14})^{\frac13}\right\}\cdot\frac{3}{2^{\frac{5}{12}}}\\ &=\left\{(2^{\frac{17}{3}})^{\frac14}+(2^{\frac{17}{3}})^{\frac14}-3\cdot(2^{\frac{5}{4}})^{\frac13}\right\}\cdot\frac{3}{2^{\frac{5}{12}}}\\ &=\left(2^{\frac{17}{12}}+2^{\frac{17}{12}}-3\cdot2^{\frac{5}{12}}\right)\cdot\frac{3}{2^{\frac{5}{12}}}\\ &=\left(2\cdot 2^{\frac{17}{12}-\frac{5}{12}}-3\cdot2^{\frac{5}{12}-\frac{5}{12}}\right)\cdot 3\\ &=(2\cdot2-3\cdot1)\cdot 3=3 \end{align*}$$