簡約 (-32x^{-10}y^{15})^{1/5}

解

簡約

(- 32 x^{- 10} y^{15})^{\frac{1}{5}}

- \frac{2 y ^{3}}{x ^{2}}

解答ステップ

(- 32 x^{- 10} 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 x^{- 10} y^{15})^{\frac{1}{5}} = - (32 x^{- 10} y^{15})^{\frac{1}{5}}

= - (32 x^{- 10} y^{15})^{\frac{1}{5}}

指数の規則を適用する:

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

(32 x^{- 10} y^{15})^{\frac{1}{5}} = 3 2^{\frac{1}{5}} (x^{- 10})^{\frac{1}{5}} (y^{15})^{\frac{1}{5}}

= - 3 2^{\frac{1}{5}} (x^{- 10})^{\frac{1}{5}} (y^{15})^{\frac{1}{5}}

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

= - 2 (x^{- 10})^{\frac{1}{5}} (y^{15})^{\frac{1}{5}}

簡素化

(x^{- 10})^{\frac{1}{5}} : \frac{1}{x ^{2}}

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

簡素化

(y^{15})^{\frac{1}{5}} : y^{3}

= - 2 \cdot \frac{1}{x ^{2}} y^{3}

簡素化

2 \cdot \frac{1}{x ^{2}} y^{3} : \frac{2 y ^{3}}{x ^{2}}

= - \frac{2 y ^{3}}{x ^{2}}