簡約 \sqrt[3]{4x^3y^5}*\sqrt[3]{12y^2}

解

簡約

3 4 x^{3} y^{5} \cdot 3 12 y^{2}

236 x 3 y^{7}

解答ステップ

3 4 x^{3} y^{5} 3 12 y^{2}

簡素化

3 4 x^{3} y^{5} : 34 x y 3 y^{2}

= 34 x y 3 y^{2} 3 12 y^{2}

簡素化

3 12 y^{2} : 312 3 y^{2}

= 34 x y 3 y^{2} 312 3 y^{2}

累乗根の規則を適用する:

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

3 y^{2} = (y^{2})^{\frac{1}{3}}

= 34 x y (y^{2})^{\frac{1}{3}} 312 (y^{2})^{\frac{1}{3}}

簡素化

(y^{2})^{\frac{1}{3}} (y^{2})^{\frac{1}{3}} : y^{\frac{4}{3}}

= 34 x y y^{\frac{4}{3}} 312

34312 = 348

= 348 x y y^{\frac{4}{3}}

348 = 236

= 236 x y y^{\frac{4}{3}}

簡素化

y y^{\frac{4}{3}} : y^{\frac{7}{3}}

= 236 x y^{\frac{7}{3}}

y^{\frac{7}{3}} = 3 y^{7}

= 236 x 3 y^{7}