簡約 sqrt(\sqrt[7]{xy)}× sqrt(xy)

解

簡約

7 x y \cdot x y

7 x^{4} 7 y^{4}

解答ステップ

7 x y x y

7 x y = (x y)^{\frac{1}{14}}

x y = (x y)^{\frac{1}{2}}

= (x y)^{\frac{1}{14}} (x y)^{\frac{1}{2}}

指数の規則を適用する:

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

(x y)^{\frac{1}{14}} (x y)^{\frac{1}{2}} = (x y)^{\frac{1}{14} + \frac{1}{2}}

= (x y)^{\frac{1}{14} + \frac{1}{2}}

\frac{1}{14} + \frac{1}{2} = \frac{4}{7}

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

指数の規則を適用する:

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

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

= x^{\frac{4}{7}} y^{\frac{4}{7}}

x^{\frac{4}{7}} = 7 x^{4}

= 7 x^{4} 7 y^{4}

y^{\frac{4}{7}} = 7 y^{4}

= 7 x^{4} 7 y^{4}