簡約 (-3a^2b^4c^6)^2

解

簡約

(- 3 a^{2} b^{4} c^{6})^{2}

9 a^{4} b^{8} c^{12}

解答ステップ

(- 3 a^{2} b^{4} c^{6})^{2}

指数の規則を適用する:

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

(

n

が偶数の場合)

(- 3 a^{2} b^{4} c^{6})^{2} = (3 a^{2} b^{4} c^{6})^{2}

= (3 a^{2} b^{4} c^{6})^{2}

指数の規則を適用する:

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

(3 a^{2} b^{4} c^{6})^{2} = 3^{2} (a^{2})^{2} (b^{4})^{2} (c^{6})^{2}

= 3^{2} (a^{2})^{2} (b^{4})^{2} (c^{6})^{2}

3^{2} = 9

= 9 (a^{2})^{2} (b^{4})^{2} (c^{6})^{2}

簡素化

(a^{2})^{2} : a^{4}

= 9 a^{4} (b^{4})^{2} (c^{6})^{2}

簡素化

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

= 9 a^{4} b^{8} (c^{6})^{2}

簡素化

(c^{6})^{2} : c^{12}

= 9 a^{4} b^{8} c^{12}