簡約 (-32y^{15})^{1/5}

解

簡約

(- 32 y^{15})^{\frac{1}{5}}

- 2 y^{3}

解答ステップ

(- 32 y^{15})^{\frac{1}{5}}

指数の規則を適用する:

(- a)^{\frac{1}{n}} = - (a)^{\frac{1}{n}},

(

n

が奇数の場合)

(- 32 y^{15})^{\frac{1}{5}} = - (32 y^{15})^{\frac{1}{5}}

= - (32 y^{15})^{\frac{1}{5}}

指数の規則を適用する:

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

(32 y^{15})^{\frac{1}{5}} = 3 2^{\frac{1}{5}} (y^{15})^{\frac{1}{5}}

= - 3 2^{\frac{1}{5}} (y^{15})^{\frac{1}{5}}

3 2^{\frac{1}{5}} = 2

= - 2 (y^{15})^{\frac{1}{5}}

指数の規則を適用する:

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

, 以下を想定

a \geq 0

(y^{15})^{\frac{1}{5}} = y^{15 \cdot \frac{1}{5}}

= - 2 y^{15 \cdot \frac{1}{5}}

15 \cdot \frac{1}{5} = 3

= - 2 y^{3}