第9章 9.3

(1)

$9^{0.5} = (3^2)^{\frac{1}{2}} = 3$

(2)

$32^{0.4} = (2^5)^{\frac{2}{5}} = 2^2 = 4$

(3)

$81^{\frac{1}{4}} = (3^4)^{\frac{1}{4}} = 3$

(4)

$27^{-\frac{2}{3}} = (3^3)^{-\frac{2}{3}} = 3^{-2} = \frac{1}{9}$

(5)

$9^2 \times 27 \div 9^3 \div \frac{1}{3} = 3^4 \times 3^3 \times 3^{-6} \times 3 = 3^2 = 9$

(6)

$10^{\frac{1}{2}} \times 5^{-\frac{1}{2}} \times 2^{\frac{1}{2}} = 4^{\frac{1}{2}} = 2$

(7)

$0.0025^{-1.5} = \left(\frac{5^2}{10^4}\right)^{-\frac{3}{2}} = (4^2 5^2)^{\frac{3}{2}} = 4^3 5^3 = 20^3 = 8000$