簡約 (-4x^2y^3)^4

解

簡約

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

256 x^{8} y^{12}

解答ステップ

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

指数の規則を適用する:

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

(

n

が偶数の場合)

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

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

指数の規則を適用する:

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

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

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

4^{4} = 256

= 256 (x^{2})^{4} (y^{3})^{4}

簡素化

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

= 256 x^{8} (y^{3})^{4}

簡素化

(y^{3})^{4} : y^{12}

= 256 x^{8} y^{12}