簡約 (7^2x^3)^2

解

簡約

(7^{2} x^{3})^{2}

2401 x^{6}

解答ステップ

(7^{2} x^{3})^{2}

指数の規則を適用する:

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

(7^{2} x^{3})^{2} = (7^{2})^{2} (x^{3})^{2}

= (7^{2})^{2} (x^{3})^{2}

(7^{2})^{2} = 2401

= 2401 (x^{3})^{2}

指数の規則を適用する:

(a^{b})^{c} = a^{b c},

, 以下を想定

a \geq 0

(x^{3})^{2} = x^{3 \cdot 2}

= 2401 x^{3 \cdot 2}

数を乗じる:

3 \cdot 2 = 6

= 2401 x^{6}