簡約 (2a^3b^5c^2)^4

解

簡約

(2 a^{3} \cdot b^{5} \cdot c^{2})^{4}

16 a^{12} b^{20} c^{8}

解答ステップ

(2 a^{3} b^{5} c^{2})^{4}

指数の規則を適用する:

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

(2 a^{3} b^{5} c^{2})^{4} = 2^{4} (a^{3})^{4} (b^{5})^{4} (c^{2})^{4}

= 2^{4} (a^{3})^{4} (b^{5})^{4} (c^{2})^{4}

2^{4} = 16

= 16 (a^{3})^{4} (b^{5})^{4} (c^{2})^{4}

簡素化

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

= 16 a^{12} (b^{5})^{4} (c^{2})^{4}

簡素化

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

= 16 a^{12} b^{20} (c^{2})^{4}

簡素化

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

= 16 a^{12} b^{20} c^{8}