化简 \sqrt[3]{36}(1.64(0.082)^2)^{1/3}

解答

化简

336 \cdot (1.64 \cdot (0.082)^{2})^{\frac{1}{3}}

\frac{41}{25 \cdot 2 5 ^{\frac{1}{3}} \cdot 4 ^{\frac{2}{3}}} 336

十进制

0.73495 \dots

求解步骤

336 (1.64 \cdot 0.08 2^{2})^{\frac{1}{3}}

使用指数法则:

(a \cdot b)^{n} = a^{n} b^{n}

(1.64 \cdot 0.08 2^{2})^{\frac{1}{3}} = 1.6 4^{\frac{1}{3}} (0.08 2^{2})^{\frac{1}{3}}

= 336 \cdot 1.6 4^{\frac{1}{3}} (0.08 2^{2})^{\frac{1}{3}}

1.64 = \frac{41}{25}

= 336 (\frac{41}{25})^{\frac{1}{3}} (0.08 2^{2})^{\frac{1}{3}}

(0.08 2^{2})^{\frac{1}{3}} = \frac{4 1 ^{\frac{2}{3}}}{25 \cdot 4 ^{\frac{2}{3}}}

= 336 (\frac{41}{25})^{\frac{1}{3}} \frac{4 1 ^{\frac{2}{3}}}{25 \cdot 4 ^{\frac{2}{3}}}

(\frac{41}{25})^{\frac{1}{3}} \frac{4 1 ^{\frac{2}{3}}}{25 \cdot 4 ^{\frac{2}{3}}} = \frac{41}{25 \cdot 2 5 ^{\frac{1}{3}} \cdot 4 ^{\frac{2}{3}}}

= 336 \frac{41}{25 \cdot 2 5 ^{\frac{1}{3}} \cdot 4 ^{\frac{2}{3}}}

= \frac{41}{25 \cdot 2 5 ^{\frac{1}{3}} \cdot 4 ^{\frac{2}{3}}} 336

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