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受欢迎的代数 >

化简 \sqrt[3]{4b}*\sqrt[3]{4b}^2

解答

化简

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

解答

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

求解步骤

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}}

分解整数

4 = 2^{2}

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

使用指数法则:

(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}}

整理后得

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

分解整数

4 = 2^{2}

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

使用指数法则:

(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}}

整理后得

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

使用指数法则:

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}}

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