Монгол Бодлогын Сан

Заавар: $a,b>0$ үед $a^{-n}=\dfrac{1}{a^n}$, $a^{\frac{m}{n}}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, $\sqrt[n]{\dfrac{a}{b}}=\dfrac{\sqrt[n]{a}}{\sqrt[n]{b}}$ болохыг ашигла.

Бодолт: $$\begin{align*} \text{Илэрх.}&=\left(\dfrac14\right)^{-\frac32}+3\cdot0.0081^{-\frac14}+\left(\dfrac1{16}\right)^{-0.75}\\ &=\left(\dfrac14\right)^{-\frac32}+3\cdot\left(\dfrac{81}{10000}\right)^{-\frac14}+\left(\dfrac1{16}\right)^{-\frac34}\\ &=4^{\frac32}+3\cdot\left(\dfrac{10000}{81}\right)^{\frac14}+16^{\frac34}\\ &=(\sqrt{4})^3+3\cdot\dfrac{\sqrt[4]{10000}}{\sqrt[4]{81}}+(\sqrt[4]{16})^3\\ &=2^3+3\cdot\dfrac{10}{3}+2^3=26 \end{align*}$$