第9章 9.12

(1)

$\sqrt{15} \times \sqrt[4]{5} \times \sqrt[4]{45} = \sqrt{15} \times \sqrt[4]{5^2 3^2} = \sqrt{15} \times \sqrt{15} = 15$

(2)

$\sqrt[3]{16} + 2\sqrt[6]{4} - 3\sqrt[9]{8} = \sqrt[3]{2^4} + 2\sqrt[3]{2} - 3\sqrt[3]{2} = 2\sqrt[3]{2} + 2\sqrt[3]{2} - 3\sqrt[3]{2} = \sqrt[3]{2}$

(3)

$\sqrt[3]{16} + \sqrt[3]{54} - \sqrt[3]{\frac{1}{4}} = 2\sqrt[3]{2} + 3\sqrt[3]{2} - \frac{1}{\sqrt[3]{2^2}} = 5\sqrt[3]{2} - \frac{\sqrt[3]{2}}{2} = \frac{9}{2}\sqrt[3]{2}$

(4)

$\left(\sqrt[3]{2} \times 2 \div \sqrt{2^3}\right)^{-6} = \left(2^{\frac{1}{3}} \times 2 \times 2^{-\frac{3}{2}}\right)^{-6} = \left(2^{-\frac{1}{6}}\right)^{-6} = 2$