化简 4/(3\sqrt[3]{x^2)}

解答

化简

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

\frac{4 3 x}{3 x}

求解步骤

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

乘以共轭根式

\frac{( x ^{2} ) ^{\frac{2}{3}}}{( x ^{2} ) ^{\frac{2}{3}}}

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

化简

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

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

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

x^{\frac{4}{3}} = x^{1 + \frac{1}{3}}, x^{2} = x^{1 + 1}

= \frac{4 x ^{\frac{1}{3} + 1}}{3 x ^{1 + 1}}

使用指数法则:

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

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

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

约分:

x^{1}

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

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

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

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