簡約 sqrt((16sin^2(x))^3)

解

簡約

(16 sin^{2} (x))^{3}

64 sin^{3} (x)

解答ステップ

(16 sin^{2} (x))^{3}

累乗根の規則を適用する:

a = a^{\frac{1}{2}}

= ((16 sin^{2} (x))^{3})^{\frac{1}{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

= (16 sin^{2} (x))^{3 \cdot \frac{1}{2}}

3 \cdot \frac{1}{2} = \frac{3}{2}

= (16 sin^{2} (x))^{\frac{3}{2}}

指数の規則を適用する:

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

= 1 6^{\frac{3}{2}} (sin^{2} (x))^{\frac{3}{2}}

1 6^{\frac{3}{2}} = 64

= 64 (sin^{2} (x))^{\frac{3}{2}}

(sin^{2} (x))^{\frac{3}{2}} : sin^{3} (x)

= 64 sin^{3} (x)