簡約 (\sqrt[3]{8x^7y^6})(\sqrt[3]{8x^7y^6})

解

簡約

(3 8 x^{7} y^{6}) (3 8 x^{7} y^{6})

4 3 x^{14} y^{4}

解答ステップ

(3 8 x^{7} y^{6}) (3 8 x^{7} y^{6})

規則を適用する:

(a) = a

(3 8 x^{7} y^{6}) = 3 8 x^{7} y^{6}

= 3 8 x^{7} y^{6} 3 8 x^{7} y^{6}

累乗根の規則を適用する:

n a = a^{\frac{1}{n}}

3 8 x^{7} y^{6} = (8 x^{7} y^{6})^{\frac{1}{3}}

= (8 x^{7} y^{6})^{\frac{1}{3}} (8 x^{7} y^{6})^{\frac{1}{3}}

指数の規則を適用する:

a^{b} \cdot a^{c} = a^{b + c}

(8 x^{7} y^{6})^{\frac{1}{3}} (8 x^{7} y^{6})^{\frac{1}{3}} = (8 x^{7} y^{6})^{\frac{1}{3} + \frac{1}{3}}

= (8 x^{7} y^{6})^{\frac{1}{3} + \frac{1}{3}}

\frac{1}{3} + \frac{1}{3} = \frac{2}{3}

= (8 x^{7} y^{6})^{\frac{2}{3}}

指数の規則を適用する:

(a \cdot b)^{n} = a^{n} b^{n}

(8 x^{7} y^{6})^{\frac{2}{3}} = 8^{\frac{2}{3}} (x^{7})^{\frac{2}{3}} (y^{6})^{\frac{2}{3}}

= 8^{\frac{2}{3}} (x^{7})^{\frac{2}{3}} (y^{6})^{\frac{2}{3}}

8^{\frac{2}{3}} = 4

= 4 (x^{7})^{\frac{2}{3}} (y^{6})^{\frac{2}{3}}

簡素化

(x^{7})^{\frac{2}{3}} : x^{\frac{14}{3}}

= 4 x^{\frac{14}{3}} (y^{6})^{\frac{2}{3}}

簡素化

(y^{6})^{\frac{2}{3}} : y^{4}

= 4 x^{\frac{14}{3}} y^{4}

x^{\frac{14}{3}} = 3 x^{14}

= 4 3 x^{14} y^{4}