簡約 (9cos^7(t))^2

解

簡約

(9 cos^{7} (t))^{2}

81 cos^{14} (t)

解答ステップ

(9 cos^{7} (t))^{2}

指数の規則を適用する:

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

(9 cos^{7} (t))^{2} = 9^{2} (cos^{7} (t))^{2}

= 9^{2} (cos^{7} (t))^{2}

9^{2} = 81

= 81 (cos^{7} (t))^{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

(cos^{7} (t))^{2} = cos^{7 \cdot 2} (t)

= 81 cos^{7 \cdot 2} (t)

数を乗じる:

7 \cdot 2 = 14

= 81 cos^{14} (t)