簡約 \sqrt[3]{a^2b}\sqrt[3]{64a^4b}

解

簡約

3 a^{2} b 3 64 a^{4} b

4 3 b^{2} 3 a^{4} 3 a^{2}

解答ステップ

3 a^{2} b 3 64 a^{4} b

簡素化

3 a^{2} b : 3 a^{2} 3 b

= 3 a^{2} 3 b 3 64 a^{4} b

簡素化

3 64 a^{4} b : 4 a 3 a 3 b

= 3 a^{2} 3 b \cdot 4 a 3 a 3 b

累乗根の規則を適用する:

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

3 b = b^{\frac{1}{3}}

= 3 a^{2} b^{\frac{1}{3}} \cdot 4 a 3 a b^{\frac{1}{3}}

簡素化

b^{\frac{1}{3}} b^{\frac{1}{3}} : b^{\frac{2}{3}}

= 3 a^{2} b^{\frac{2}{3}} \cdot 4 a 3 a

簡素化

a 3 a : a^{\frac{4}{3}}

= 3 a^{2} b^{\frac{2}{3}} \cdot 4 a^{\frac{4}{3}}

= 4 b^{\frac{2}{3}} a^{\frac{4}{3}} 3 a^{2}

b^{\frac{2}{3}} = 3 b^{2}

= 4 3 b^{2} 3 a^{4} 3 a^{2}

a^{\frac{4}{3}} = 3 a^{4}

= 4 3 b^{2} 3 a^{4} 3 a^{2}