(-0.04^1.85)674.1740

asked by guest
on Nov 18, 2024 at 2:24 pm



You asked:

Evaluate the expression: \(-{0.04}^{1.85} \cdot 674.1740\)

MathBot Answer:

\[-{0.04}^{1.85} \cdot 674.1740 = - \frac{337087 \cdot 5^{\frac{3}{10}}}{312500} \approx -1.74816726466999427512819561974957\]

\[\begin{aligned}-{0.04}^{1.85} \cdot 674.1740& = - \cdot \left(\frac{4}{100}\right)^{1 + \frac{85}{100}} \cdot \left(674 + \frac{174}{1000}\right)\\& = - \cdot \left(\frac{1}{25}\right)^{1 + \frac{85}{100}} \cdot \left(674 + \frac{174}{1000}\right)\\& = - \cdot \left(\frac{1}{25}\right)^{1 + \frac{17}{20}} \cdot \left(674 + \frac{174}{1000}\right)\\& = - \cdot \left(\frac{1}{25}\right)^{\frac{37}{20}} \cdot \left(674 + \frac{174}{1000}\right)\\& = - \cdot \frac{1}{625} \cdot 5^{\frac{3}{10}} \cdot \left(674 + \frac{174}{1000}\right)\\& = - \cdot \frac{1}{625} \cdot 5^{\frac{3}{10}} \cdot \left(674 + \frac{87}{500}\right)\\& = - \cdot \frac{1}{625} \cdot 5^{\frac{3}{10}} \cdot \frac{337087}{500}\\& = - \frac{1}{625} \cdot 5^{\frac{3}{10}} \cdot \frac{337087}{500}\\& = - \frac{337087}{312500} \cdot 5^{\frac{3}{10}}\end{aligned}\]

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