化简 \sqrt[8]{(4^3)}^7

解答

化简

8 (4^{3})^{7}

3242

十进制

38.05462 \dots

求解步骤

(8 (4^{3}))^{7}

8 (4^{3}) : 4^{\frac{3}{8}}

= (4^{\frac{3}{8}})^{7}

使用指数法则:

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

= 4^{\frac{3}{8} \cdot 7}

\frac{3}{8} \cdot 7 = \frac{21}{8}

= 4^{\frac{21}{8}}

4^{\frac{21}{8}} = 2^{\frac{21}{4}}

= 2^{\frac{21}{4}}

2^{\frac{21}{4}} = 2^{5} 42

= 2^{5} 42

2^{5} = 32

= 3242

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