簡約 (5x^2y^2m^3*n)^4

解

簡約

(5 x^{2} \cdot y^{2} \cdot m^{3} \cdot n)^{4}

625 x^{8} y^{8} m^{12} n^{4}

解答ステップ

(5 x^{2} y^{2} m^{3} n)^{4}

指数の規則を適用する:

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

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

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

5^{4} = 625

= 625 (x^{2})^{4} (y^{2})^{4} (m^{3})^{4} n^{4}

簡素化

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

= 625 x^{8} (y^{2})^{4} (m^{3})^{4} n^{4}

簡素化

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

= 625 x^{8} y^{8} (m^{3})^{4} n^{4}

簡素化

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

= 625 x^{8} y^{8} m^{12} n^{4}