簡約 (-5m^6n^8)^4

解

簡約

(- 5 m^{6} n^{8})^{4}

625 m^{24} n^{32}

解答ステップ

(- 5 m^{6} n^{8})^{4}

指数の規則を適用する:

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

(

n

が偶数の場合)

(- 5 m^{6} n^{8})^{4} = (5 m^{6} n^{8})^{4}

= (5 m^{6} n^{8})^{4}

指数の規則を適用する:

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

(5 m^{6} n^{8})^{4} = 5^{4} (m^{6})^{4} (n^{8})^{4}

= 5^{4} (m^{6})^{4} (n^{8})^{4}

5^{4} = 625

= 625 (m^{6})^{4} (n^{8})^{4}

簡素化

(m^{6})^{4} : m^{24}

= 625 m^{24} (n^{8})^{4}

簡素化

(n^{8})^{4} : n^{32}

= 625 m^{24} n^{32}