6.95* 98.411.598.41^{1.5}/ 917−0.385917^{-0.385}

asked by guest
on Mar 21, 2025 at 4:37 am



You asked:

Evaluate the expression: 6.95⋅98.411.5917−0.385\frac{6.95 \cdot {98.41}^{1.5}}{{917}^{-0.385}}

MathBot Answer:

6.95⋅98.411.5917−0.385=1367899⋅91777200984120000≈93768.2577084587898572365897277944547\frac{6.95 \cdot {98.41}^{1.5}}{{917}^{-0.385}} = \frac{1367899 \cdot 917^{\frac{77}{200}} \sqrt{9841}}{20000} \approx 93768.2577084587898572365897277944547

6.95⋅98.411.5917−0.385=(6+95100)⋅(98+41100)1+510⋅1917−3851000=(6+1920)⋅(98+41100)1+510⋅1917−3851000=13920⋅(98+41100)1+510⋅1917−3851000=13920⋅(9841100)1+510⋅1917−3851000=13920⋅(9841100)1+12⋅1917−3851000=13920⋅(9841100)32⋅1917−3851000=13920⋅98411000⋅9841⋅1917−3851000=13920⋅98411000⋅9841⋅1917−77200=13920⋅98411000⋅9841⋅1191777200=13920⋅98411000⋅9841⋅11917⋅917123200=13920⋅98411000⋅91777200⋅9841=136789920000⋅91777200⋅9841\begin{aligned}\frac{6.95 \cdot {98.41}^{1.5}}{{917}^{-0.385}}&=\left(6 + \frac{95}{100}\right) \cdot \left(98 + \frac{41}{100}\right)^{1 + \frac{5}{10}} \cdot \frac{1}{917^{- \frac{385}{1000}}}\\&=\left(6 + \frac{19}{20}\right) \cdot \left(98 + \frac{41}{100}\right)^{1 + \frac{5}{10}} \cdot \frac{1}{917^{- \frac{385}{1000}}}\\&=\frac{139}{20} \cdot \left(98 + \frac{41}{100}\right)^{1 + \frac{5}{10}} \cdot \frac{1}{917^{- \frac{385}{1000}}}\\&=\frac{139}{20} \cdot \left(\frac{9841}{100}\right)^{1 + \frac{5}{10}} \cdot \frac{1}{917^{- \frac{385}{1000}}}\\&=\frac{139}{20} \cdot \left(\frac{9841}{100}\right)^{1 + \frac{1}{2}} \cdot \frac{1}{917^{- \frac{385}{1000}}}\\&=\frac{139}{20} \cdot \left(\frac{9841}{100}\right)^{\frac{3}{2}} \cdot \frac{1}{917^{- \frac{385}{1000}}}\\&=\frac{139}{20} \cdot \frac{9841}{1000} \cdot \sqrt{9841} \cdot \frac{1}{917^{- \frac{385}{1000}}}\\&=\frac{139}{20} \cdot \frac{9841}{1000} \cdot \sqrt{9841} \cdot \frac{1}{917^{- \frac{77}{200}}}\\&=\frac{139}{20} \cdot \frac{9841}{1000} \cdot \sqrt{9841} \cdot \frac{1}{\frac{1}{917^{\frac{77}{200}}}}\\&=\frac{139}{20} \cdot \frac{9841}{1000} \cdot \sqrt{9841} \cdot \frac{1}{\frac{1}{917} \cdot 917^{\frac{123}{200}}}\\&=\frac{139}{20} \cdot \frac{9841}{1000} \cdot 917^{\frac{77}{200}} \cdot \sqrt{9841}\\&=\frac{1367899}{20000} \cdot 917^{\frac{77}{200}} \cdot \sqrt{9841}\end{aligned}

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