簡約 (\sqrt[4]{8xy^2})^2

解

簡約

(4 8 x y^{2})^{2}

22 y x

解答ステップ

(4 8 x y^{2})^{2}

累乗根の規則を適用する:

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

= ((8 x y^{2})^{\frac{1}{4}})^{2}

指数の規則を適用する:

(a^{b})^{c} = a^{b c}

= (8 x y^{2})^{\frac{1}{4} \cdot 2}

\frac{1}{4} \cdot 2 = \frac{1}{2}

= (8 x y^{2})^{\frac{1}{2}}

a^{\frac{1}{2}} = a

= 8 x y^{2}

累乗根の規則を適用する:

n ab = n a n b,

, 以下を想定

a \geq 0, b \geq 0

= 8 x y^{2}

8 = 22

= 22 x y^{2}

累乗根の規則を適用する:

n a^{n} = a,

, 以下を想定

a \geq 0

y^{2} = y

= 22 y x