簡約 (-5x^{-3}y^4)^2

解

簡約

(- 5 x^{- 3} y^{4})^{2}

\frac{25 y ^{8}}{x ^{6}}

解答ステップ

(- 5 x^{- 3} y^{4})^{2}

指数の規則を適用する:

(- a)^{n} = a^{n},

(

n

が偶数の場合)

(- 5 x^{- 3} y^{4})^{2} = (5 x^{- 3} y^{4})^{2}

= (5 x^{- 3} y^{4})^{2}

指数の規則を適用する:

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

(5 x^{- 3} y^{4})^{2} = 5^{2} (x^{- 3})^{2} (y^{4})^{2}

= 5^{2} (x^{- 3})^{2} (y^{4})^{2}

5^{2} = 25

= 25 (x^{- 3})^{2} (y^{4})^{2}

簡素化

(x^{- 3})^{2} : \frac{1}{x ^{6}}

= 25 \cdot \frac{1}{x ^{6}} (y^{4})^{2}

簡素化

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

= 25 \cdot \frac{1}{x ^{6}} y^{8}

簡素化

25 \cdot \frac{1}{x ^{6}} y^{8} : \frac{25 y ^{8}}{x ^{6}}

= \frac{25 y ^{8}}{x ^{6}}