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受欢迎的代数 >

化简 (16x^2)^{1/3}(\sqrt[3]{4x})

解答

化简

(16 x^{2})^{\frac{1}{3}} (3 4 x)

解答

4 x

求解步骤

(16 x^{2})^{\frac{1}{3}} (3 4 x)

使用法则:

(a) = a

(3 4 x) = 3 4 x

= (16 x^{2})^{\frac{1}{3}} 3 4 x

化简

(16 x^{2})^{\frac{1}{3}} : 2 \cdot 2^{\frac{1}{3}} x^{\frac{2}{3}}

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

化简

3 4 x : 34 3 x

= 2 \cdot 2^{\frac{1}{3}} x^{\frac{2}{3}} 34 3 x

使用根式运算法则:

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

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

= 2 \cdot 2^{\frac{1}{3}} x^{\frac{2}{3}} 34 x^{\frac{1}{3}}

化简

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

= 2 \cdot 2^{\frac{1}{3}} x 34

= 2 \cdot 2^{\frac{1}{3}} 34 x

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

= 2^{\frac{4}{3}} 34 x

分解整数

4 = 2^{2}

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

使用指数法则:

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

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

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

整理后得

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

使用指数法则:

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

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

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

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

= 2^{2} x

2^{2} = 4

= 4 x

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