第9章 9.7

(1)

$16^{\frac{1}{2}} = (4^2)^{\frac{1}{2}} = 4$

(2)

$\left(\frac{9}{25}\right)^{\frac{1}{2}} = \left(\frac{3^2}{5^2}\right)^{\frac{1}{2}} = \frac{3}{5}$

(3)

$6^{-2} = \frac{1}{36}$

(4)

$\left(\frac{4}{5}\right)^{2} = \frac{16}{25}$

(5)

$8^0 = 1$

(6)

$2.4 \times 10^3 = 2.4 \times 1000 = 2400$

(7)

$25^{-\frac{1}{2}} = (5^2)^{-\frac{1}{2}} = \frac{1}{5}$

(8)

$625^{\frac{3}{4}} = (5^4)^{\frac{3}{4}} = 5^3 = 125$

(9)

$16^{-\frac{3}{4}} = (2^4)^{-\frac{3}{4}} = 2^{-3} = \frac{1}{8}$

(10)

$12^{\frac{1}{2}} \cdot 3^{\frac{3}{2}} = (3^4 \cdot 2^2)^{\frac{1}{2}} = 3^2 \cdot 2 = 18$

(11)

$\frac{\sqrt[3]{24}}{\sqrt[3]{3}} = \sqrt[3]{8} = \sqrt[3]{2^3} = 2$

(12)

$\sqrt[5]{-32} = \sqrt[5]{(-2)^5} = -2$