第9章 9.6

(1)

$2^{\frac{1}{3}} = \sqrt[3]{2}$

(2)

$15^{\frac{2}{5}} = \sqrt[5]{15^2}$

(3)

$(4x)^{\frac{4}{5}} = \sqrt[5]{(4x)^4}$

(4)

$10^{0.5} = 10^{\frac{1}{2}} = \sqrt{10}$

(5)

$10^{0.3} = 10^{\frac{3}{10}} = \sqrt[10]{10^3}$

(6)

$5^{1.2} = 5^{\frac{6}{5}} = \sqrt[5]{5^6}$

(7)

$(2x^2)^{2.3} = (2x^2)^{\frac{23}{10}} = \sqrt[10]{(2x^2)^{23}}$

(8)

$(x^{-1}y)^{-\frac{1}{2}} = \left(\frac{x}{y}\right)^{\frac{1}{2}} = \sqrt{\frac{x}{y}}$

(9)

$(2x)^{-0.2} = (2x)^{-\frac{1}{5}} = \sqrt[5]{\frac{1}{2x}}$

(10)

$(16x)^{0.75} = (16x)^{\frac{3}{4}} = \sqrt[4]{(16x)^3} = \sqrt[4]{(2^3)^4 x^3} = 2^3\sqrt[4]{x^3} = 8\sqrt[4]{x^3}$