5.3(37.4)+0.16((37.4-39.9)/(-0.24))^(3/2)

asked by guest
on Mar 16, 2025 at 5:34 am



You asked:

Evaluate the expression: 5.3⋅37.4+0.16(37.4−39.9−0.24)325.3 \cdot 37.4 + 0.16 {\left( \frac{37.4 - 39.9}{-0.24} \right)}^{\frac{3}{2}}

MathBot Answer:

5.3⋅37.4+0.16(37.4−39.9−0.24)32=251518+991150≈203.599143536399190118304535277475565.3 \cdot 37.4 + 0.16 {\left( \frac{37.4 - 39.9}{-0.24} \right)}^{\frac{3}{2}} = \frac{25 \sqrt{15}}{18} + \frac{9911}{50} \approx 203.59914353639919011830453527747556

5.3⋅37.4+0.16(37.4−39.9−0.24)32=(5+310)⋅(37+410)+16100⋅((37+410−(39+910))⋅1−24100)32=5310⋅(37+410)+16100⋅((37+410−(39+910))⋅1−24100)32=5310⋅(37+25)+16100⋅((37+410−(39+910))⋅1−24100)32=5310⋅1875+16100⋅((37+410−(39+910))⋅1−24100)32=991150+16100⋅((37+410−(39+910))⋅1−24100)32=991150+16100⋅((37+25−(39+910))⋅1−24100)32=991150+16100⋅((37+25−39910)⋅1−24100)32=991150+16100⋅((1875−39910)⋅1−24100)32=991150+16100⋅(−52⋅1−24100)32=991150+16100⋅(−52⋅1−625)32=991150+16100⋅(12512)32=991150+16100⋅62572⋅15=991150+425⋅62572⋅15=991150+2518⋅15\begin{aligned}5.3 \cdot 37.4 + 0.16 {\left( \frac{37.4 - 39.9}{-0.24} \right)}^{\frac{3}{2}}&=\left(5 + \frac{3}{10}\right) \cdot \left(37 + \frac{4}{10}\right) + \frac{16}{100} \cdot \left(\left(37 + \frac{4}{10} - \left(39 + \frac{9}{10}\right)\right) \cdot \frac{1}{- \frac{24}{100}}\right)^{\frac{3}{2}}\\&=\frac{53}{10} \cdot \left(37 + \frac{4}{10}\right) + \frac{16}{100} \cdot \left(\left(37 + \frac{4}{10} - \left(39 + \frac{9}{10}\right)\right) \cdot \frac{1}{- \frac{24}{100}}\right)^{\frac{3}{2}}\\&=\frac{53}{10} \cdot \left(37 + \frac{2}{5}\right) + \frac{16}{100} \cdot \left(\left(37 + \frac{4}{10} - \left(39 + \frac{9}{10}\right)\right) \cdot \frac{1}{- \frac{24}{100}}\right)^{\frac{3}{2}}\\&=\frac{53}{10} \cdot \frac{187}{5} + \frac{16}{100} \cdot \left(\left(37 + \frac{4}{10} - \left(39 + \frac{9}{10}\right)\right) \cdot \frac{1}{- \frac{24}{100}}\right)^{\frac{3}{2}}\\&=\frac{9911}{50} + \frac{16}{100} \cdot \left(\left(37 + \frac{4}{10} - \left(39 + \frac{9}{10}\right)\right) \cdot \frac{1}{- \frac{24}{100}}\right)^{\frac{3}{2}}\\&=\frac{9911}{50} + \frac{16}{100} \cdot \left(\left(37 + \frac{2}{5} - \left(39 + \frac{9}{10}\right)\right) \cdot \frac{1}{- \frac{24}{100}}\right)^{\frac{3}{2}}\\&=\frac{9911}{50} + \frac{16}{100} \cdot \left(\left(37 + \frac{2}{5} - \frac{399}{10}\right) \cdot \frac{1}{- \frac{24}{100}}\right)^{\frac{3}{2}}\\&=\frac{9911}{50} + \frac{16}{100} \cdot \left(\left(\frac{187}{5} - \frac{399}{10}\right) \cdot \frac{1}{- \frac{24}{100}}\right)^{\frac{3}{2}}\\&=\frac{9911}{50} + \frac{16}{100} \cdot \left(- \frac{5}{2} \cdot \frac{1}{- \frac{24}{100}}\right)^{\frac{3}{2}}\\&=\frac{9911}{50} + \frac{16}{100} \cdot \left(- \frac{5}{2} \cdot \frac{1}{- \frac{6}{25}}\right)^{\frac{3}{2}}\\&=\frac{9911}{50} + \frac{16}{100} \cdot \left(\frac{125}{12}\right)^{\frac{3}{2}}\\&=\frac{9911}{50} + \frac{16}{100} \cdot \frac{625}{72} \cdot \sqrt{15}\\&=\frac{9911}{50} + \frac{4}{25} \cdot \frac{625}{72} \cdot \sqrt{15}\\&=\frac{9911}{50} + \frac{25}{18} \cdot \sqrt{15}\end{aligned}

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