化简 (57.8)^{1/2}x(0.0027)^{1/3}

解答

化简

(57.8)^{\frac{1}{2}} x (0.0027)^{\frac{1}{3}}

\frac{51 x}{10 \cdot 5 ^{\frac{5}{6}} \cdot 2 ^{\frac{1}{3}}}

求解步骤

57. 8^{\frac{1}{2}} x \cdot 0.002 7^{\frac{1}{3}}

57. 8^{\frac{1}{2}} = \frac{17}{5 ^{\frac{1}{2}}}

= \frac{17}{5 ^{\frac{1}{2}}} x \cdot 0.002 7^{\frac{1}{3}}

0.002 7^{\frac{1}{3}} = \frac{3}{10 \cdot 1 0 ^{\frac{1}{3}}}

= \frac{17}{5 ^{\frac{1}{2}}} x \frac{3}{10 \cdot 1 0 ^{\frac{1}{3}}}

使用分式法则:

a \cdot \frac{b}{c} \cdot \frac{d}{e} = \frac{a \cdot b \cdot d}{c \cdot e}

= \frac{17 x \cdot 3}{5 ^{\frac{1}{2}} \cdot 10 \cdot 1 0 ^{\frac{1}{3}}}

数字相乘:

17 \cdot 3 = 51

= \frac{51 x}{5 ^{\frac{1}{2}} \cdot 10 \cdot 1 0 ^{\frac{1}{3}}}

5^{\frac{1}{2}} \cdot 10 \cdot 1 0^{\frac{1}{3}} = 10 \cdot 5^{\frac{5}{6}} \cdot 2^{\frac{1}{3}}

= \frac{51 x}{10 \cdot 5 ^{\frac{5}{6}} \cdot 2 ^{\frac{1}{3}}}

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