化简 (\sqrt[6]{5sqrt(2)-7})^3

解答

化简

(6 52 - 7)^{3}

52 - 7

十进制

0.26658 \dots

求解步骤

(6 52 - 7)^{3}

使用根式运算法则:

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

= ((52 - 7)^{\frac{1}{6}})^{3}

使用指数法则:

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

= (52 - 7)^{\frac{1}{6} \cdot 3}

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

= (52 - 7)^{\frac{1}{2}}

a^{\frac{1}{2}} = a

= 52 - 7

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