簡約 \sqrt[3]{4b}*\sqrt[3]{4b}^2

解

簡約

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

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

解答ステップ

3 4 b (3 4 b)^{2}

(3 4 b)^{2} : (4 b)^{\frac{2}{3}}

= 3 4 b (4 b)^{\frac{2}{3}}

3 4 b = 34 3 b

= 34 3 b (4 b)^{\frac{2}{3}}

(4 b)^{\frac{2}{3}} = 4^{\frac{2}{3}} b^{\frac{2}{3}}

= 34 \cdot 4^{\frac{2}{3}} 3 b b^{\frac{2}{3}}

整数を因数分解する

4 = 2^{2}

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

指数の規則を適用する:

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

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

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

改良

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

整数を因数分解する

4 = 2^{2}

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

指数の規則を適用する:

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

(2^{2})^{\frac{2}{3}} = 2^{2 \cdot \frac{2}{3}}

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

改良

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

指数の規則を適用する:

a^{b} \cdot a^{c} = a^{b + c}

2^{\frac{2}{3}} \cdot 2^{\frac{4}{3}} = 2^{\frac{2}{3} + \frac{4}{3}}

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

2^{\frac{2}{3} + \frac{4}{3}} = 2^{2}

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

2^{2} = 4

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