簡約 (5x^2y^4)^5

解

簡約

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

3125 x^{10} y^{20}

解答ステップ

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

指数の規則を適用する:

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

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

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

5^{5} = 3125

= 3125 (x^{2})^{5} (y^{4})^{5}

簡素化

(x^{2})^{5} : x^{10}

= 3125 x^{10} (y^{4})^{5}

簡素化

(y^{4})^{5} : y^{20}

= 3125 x^{10} y^{20}