簡約 \sqrt[5]{[(6c+7)^{15}(d+1)^{45}]^3}

解

簡約

5 [(6 c + 7)^{15} (d + 1)^{45}]^{3}

(d + 1)^{27} (6 c + 7)^{9}

解答ステップ

5 [(6 c + 7)^{15} (d + 1)^{45}]^{3}

累乗根の規則を適用する:

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

= ([(6 c + 7)^{15} (d + 1)^{45}]^{3})^{\frac{1}{5}}

指数の規則を適用する:

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

, 以下を想定

a \geq 0

= [(6 c + 7)^{15} (d + 1)^{45}]^{3 \cdot \frac{1}{5}}

3 \cdot \frac{1}{5} = \frac{3}{5}

= [(6 c + 7)^{15} (d + 1)^{45}]^{\frac{3}{5}}

指数の規則を適用する:

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

= ((d + 1)^{45})^{\frac{3}{5}} ((6 c + 7)^{15})^{\frac{3}{5}}

((6 c + 7)^{15})^{\frac{3}{5}} : (6 c + 7)^{9}

= (6 c + 7)^{9} ((d + 1)^{45})^{\frac{3}{5}}

((d + 1)^{45})^{\frac{3}{5}} : (d + 1)^{27}

= (6 c + 7)^{9} (d + 1)^{27}