化简 4.5*(\sqrt[3]{17.5})^2

解答

化简

4.5 \cdot (3 17.5)^{2}

4.5 3 \frac{1225}{4}

十进制

30.33224 \dots

求解步骤

4.5 (3 17.5)^{2}

17.5 = \frac{35}{2}

= 4.5 (3 \frac{35}{2})^{2}

(3 \frac{35}{2})^{2} = (\frac{35}{2})^{\frac{2}{3}}

= 4.5 (\frac{35}{2})^{\frac{2}{3}}

使用指数法则:

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

(\frac{35}{2})^{\frac{2}{3}} = \frac{3 5 ^{\frac{2}{3}}}{2 ^{\frac{2}{3}}}

= 4.5 \cdot \frac{3 5 ^{\frac{2}{3}}}{2 ^{\frac{2}{3}}}

\frac{3 5 ^{\frac{2}{3}}}{2 ^{\frac{2}{3}}} = 3 \frac{1225}{4}

= 4.5 3 \frac{1225}{4}

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