化简 sqrt(\sqrt[3]{49x^4y^2)}

解答

化简

3 49 x^{4} y^{2}

37 6 x^{4} y^{2}

求解步骤

3 49 x^{4} y^{2}

使用根式运算法则:

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

= ((49 x^{4} y^{2})^{\frac{1}{3}})^{\frac{1}{2}}

使用指数法则:

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

假定

a \geq 0

= (49 x^{4} y^{2})^{\frac{1}{3} \cdot \frac{1}{2}}

\frac{1}{3} \cdot \frac{1}{2} = \frac{1}{6}

= (49 x^{4} y^{2})^{\frac{1}{6}}

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

= 6 49 x^{4} y^{2}

使用根式运算法则:

n ab = n a n b,

假定

a \geq 0, b \geq 0

= 649 6 x^{4} y^{2}

649 = 37

= 37 6 x^{4} y^{2}

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