化简 2.910^{-4}58.33^{4/3}

解答

化简

2.9 \cdot 1 0^{- 4} \cdot 58.3 3^{\frac{4}{3}}

\frac{583 3 ^{\frac{1}{3}} \cdot 16915.7}{10 0 ^{\frac{1}{3}} \cdot 1000000}

十进制

0.06560 \dots

求解步骤

2.9 \cdot 1 0^{- 4} \cdot 58.3 3^{\frac{4}{3}}

1 0^{- 4} = \frac{1}{10000}

= 2.9 \cdot \frac{1}{10000} \cdot 58.3 3^{\frac{4}{3}}

58.33 = \frac{5833}{100}

= 2.9 \cdot \frac{1}{10000} (\frac{5833}{100})^{\frac{4}{3}}

使用指数法则:

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

(\frac{5833}{100})^{\frac{4}{3}} = \frac{583 3 ^{\frac{4}{3}}}{10 0 ^{\frac{4}{3}}}

= 2.9 \cdot \frac{1}{10000} \cdot \frac{583 3 ^{\frac{4}{3}}}{10 0 ^{\frac{4}{3}}}

\frac{583 3 ^{\frac{4}{3}}}{10 0 ^{\frac{4}{3}}} = \frac{5833 \cdot 583 3 ^{\frac{1}{3}}}{100 \cdot 10 0 ^{\frac{1}{3}}}

= 2.9 \cdot \frac{1}{10000} \cdot \frac{5833 \cdot 583 3 ^{\frac{1}{3}}}{100 \cdot 10 0 ^{\frac{1}{3}}}

2.9 \cdot \frac{1}{10000} \cdot \frac{5833 \cdot 583 3 ^{\frac{1}{3}}}{100 \cdot 10 0 ^{\frac{1}{3}}} = \frac{583 3 ^{\frac{1}{3}} \cdot 16915.7}{10 0 ^{\frac{1}{3}} \cdot 1000000}

= \frac{583 3 ^{\frac{1}{3}} \cdot 16915.7}{10 0 ^{\frac{1}{3}} \cdot 1000000}

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