3(-2/5)² - 6(-2/5) / -7(-2/5)³ + 5(-2/5)²3(-2/5)² - 6(-2/5) / -7(-2/5)³ + 5(-2/5)²

asked by guest
on Nov 18, 2024 at 3:48 am



You asked:

Evaluate the expression: \(3 \cdot {\left( \frac{-2}{5} \right)}^{2} - \frac{6 \cdot \frac{-2}{5}}{-\left( 7 \cdot {\left( \frac{-2}{5} \right)}^{3} \right)} + 5 \cdot {\left( \frac{-2}{5} \right)}^{2} \cdot 3 \cdot {\left( \frac{-2}{5} \right)}^{2} - \frac{6 \cdot \frac{-2}{5}}{-\left( 7 \cdot {\left( \frac{-2}{5} \right)}^{3} \right)} + 5 \cdot {\left( \frac{-2}{5} \right)}^{2}\)

MathBot Answer:

\[3 \cdot {\left( \frac{-2}{5} \right)}^{2} - \frac{6 \cdot \frac{-2}{5}}{-\left( 7 \cdot {\left( \frac{-2}{5} \right)}^{3} \right)} + 5 \cdot {\left( \frac{-2}{5} \right)}^{2} \cdot 3 \cdot {\left( \frac{-2}{5} \right)}^{2} - \frac{6 \cdot \frac{-2}{5}}{-\left( 7 \cdot {\left( \frac{-2}{5} \right)}^{3} \right)} + 5 \cdot {\left( \frac{-2}{5} \right)}^{2} = \frac{10831}{875} = 12.378\overline{285714}\]

\[\begin{aligned}3 \cdot {\left( \frac{-2}{5} \right)}^{2} - \frac{6 \cdot \frac{-2}{5}}{-\left( 7 \cdot {\left( \frac{-2}{5} \right)}^{3} \right)} + 5 \cdot {\left( \frac{-2}{5} \right)}^{2} \cdot 3 \cdot {\left( \frac{-2}{5} \right)}^{2} - \frac{6 \cdot \frac{-2}{5}}{-\left( 7 \cdot {\left( \frac{-2}{5} \right)}^{3} \right)} + 5 \cdot {\left( \frac{-2}{5} \right)}^{2}& = 3 \cdot \left(- \frac{2}{5}\right)^{2} - 6 \cdot - \frac{2}{5} \cdot \frac{1}{- 7 \cdot \left(- \frac{2}{5}\right)^{3}} + 5 \cdot \left(- \frac{2}{5}\right)^{2} \cdot 3 \cdot \left(- \frac{2}{5}\right)^{2} - 6 \cdot - \frac{2}{5} \cdot \frac{1}{- 7 \cdot \left(- \frac{2}{5}\right)^{3}} + 5 \cdot \left(- \frac{2}{5}\right)^{2}\\& = 3 \cdot \frac{4}{25} - 6 \cdot - \frac{2}{5} \cdot \frac{1}{- 7 \cdot \left(- \frac{2}{5}\right)^{3}} + 5 \cdot \left(- \frac{2}{5}\right)^{2} \cdot 3 \cdot \left(- \frac{2}{5}\right)^{2} - 6 \cdot - \frac{2}{5} \cdot \frac{1}{- 7 \cdot \left(- \frac{2}{5}\right)^{3}} + 5 \cdot \left(- \frac{2}{5}\right)^{2}\\& = \frac{12}{25} - 6 \cdot - \frac{2}{5} \cdot \frac{1}{- 7 \cdot \left(- \frac{2}{5}\right)^{3}} + 5 \cdot \left(- \frac{2}{5}\right)^{2} \cdot 3 \cdot \left(- \frac{2}{5}\right)^{2} - 6 \cdot - \frac{2}{5} \cdot \frac{1}{- 7 \cdot \left(- \frac{2}{5}\right)^{3}} + 5 \cdot \left(- \frac{2}{5}\right)^{2}\\& = \frac{12}{25} - 6 \cdot - \frac{2}{5} \cdot \frac{1}{- 7 \cdot - \frac{8}{125}} + 5 \cdot \left(- \frac{2}{5}\right)^{2} \cdot 3 \cdot \left(- \frac{2}{5}\right)^{2} - 6 \cdot - \frac{2}{5} \cdot \frac{1}{- 7 \cdot \left(- \frac{2}{5}\right)^{3}} + 5 \cdot \left(- \frac{2}{5}\right)^{2}\\& = \frac{12}{25} - 6 \cdot - \frac{2}{5} \cdot \frac{1}{- - \frac{56}{125}} + 5 \cdot \left(- \frac{2}{5}\right)^{2} \cdot 3 \cdot \left(- \frac{2}{5}\right)^{2} - 6 \cdot - \frac{2}{5} \cdot \frac{1}{- 7 \cdot \left(- \frac{2}{5}\right)^{3}} + 5 \cdot \left(- \frac{2}{5}\right)^{2}\\& = \frac{12}{25} - 6 \cdot - \frac{2}{5} \cdot \frac{1}{\frac{56}{125}} + 5 \cdot \left(- \frac{2}{5}\right)^{2} \cdot 3 \cdot \left(- \frac{2}{5}\right)^{2} - 6 \cdot - \frac{2}{5} \cdot \frac{1}{- 7 \cdot \left(- \frac{2}{5}\right)^{3}} + 5 \cdot \left(- \frac{2}{5}\right)^{2}\\& = \frac{12}{25} - 6 \cdot - \frac{25}{28} + 5 \cdot \left(- \frac{2}{5}\right)^{2} \cdot 3 \cdot \left(- \frac{2}{5}\right)^{2} - 6 \cdot - \frac{2}{5} \cdot \frac{1}{- 7 \cdot \left(- \frac{2}{5}\right)^{3}} + 5 \cdot \left(- \frac{2}{5}\right)^{2}\\& = \frac{12}{25} - - \frac{75}{14} + 5 \cdot \left(- \frac{2}{5}\right)^{2} \cdot 3 \cdot \left(- \frac{2}{5}\right)^{2} - 6 \cdot - \frac{2}{5} \cdot \frac{1}{- 7 \cdot \left(- \frac{2}{5}\right)^{3}} + 5 \cdot \left(- \frac{2}{5}\right)^{2}\\& = \frac{12}{25} + \frac{75}{14} + 5 \cdot \left(- \frac{2}{5}\right)^{2} \cdot 3 \cdot \left(- \frac{2}{5}\right)^{2} - 6 \cdot - \frac{2}{5} \cdot \frac{1}{- 7 \cdot \left(- \frac{2}{5}\right)^{3}} + 5 \cdot \left(- \frac{2}{5}\right)^{2}\\& = \frac{12}{25} + \frac{75}{14} + 5 \cdot \frac{4}{25} \cdot 3 \cdot \left(- \frac{2}{5}\right)^{2} - 6 \cdot - \frac{2}{5} \cdot \frac{1}{- 7 \cdot \left(- \frac{2}{5}\right)^{3}} + 5 \cdot \left(- \frac{2}{5}\right)^{2}\\& = \frac{12}{25} + \frac{75}{14} + 5 \cdot \frac{4}{25} \cdot 3 \cdot \frac{4}{25} - 6 \cdot - \frac{2}{5} \cdot \frac{1}{- 7 \cdot \left(- \frac{2}{5}\right)^{3}} + 5 \cdot \left(- \frac{2}{5}\right)^{2}\\& = \frac{12}{25} + \frac{75}{14} + \frac{4}{5} \cdot 3 \cdot \frac{4}{25} - 6 \cdot - \frac{2}{5} \cdot \frac{1}{- 7 \cdot \left(- \frac{2}{5}\right)^{3}} + 5 \cdot \left(- \frac{2}{5}\right)^{2}\\& = \frac{12}{25} + \frac{75}{14} + \frac{12}{5} \cdot \frac{4}{25} - 6 \cdot - \frac{2}{5} \cdot \frac{1}{- 7 \cdot \left(- \frac{2}{5}\right)^{3}} + 5 \cdot \left(- \frac{2}{5}\right)^{2}\\& = \frac{12}{25} + \frac{75}{14} + \frac{48}{125} - 6 \cdot - \frac{2}{5} \cdot \frac{1}{- 7 \cdot \left(- \frac{2}{5}\right)^{3}} + 5 \cdot \left(- \frac{2}{5}\right)^{2}\\& = \frac{12}{25} + \frac{75}{14} + \frac{48}{125} - 6 \cdot - \frac{2}{5} \cdot \frac{1}{- 7 \cdot - \frac{8}{125}} + 5 \cdot \left(- \frac{2}{5}\right)^{2}\\& = \frac{12}{25} + \frac{75}{14} + \frac{48}{125} - 6 \cdot - \frac{2}{5} \cdot \frac{1}{- - \frac{56}{125}} + 5 \cdot \left(- \frac{2}{5}\right)^{2}\\& = \frac{12}{25} + \frac{75}{14} + \frac{48}{125} - 6 \cdot - \frac{2}{5} \cdot \frac{1}{\frac{56}{125}} + 5 \cdot \left(- \frac{2}{5}\right)^{2}\\& = \frac{12}{25} + \frac{75}{14} + \frac{48}{125} - 6 \cdot - \frac{25}{28} + 5 \cdot \left(- \frac{2}{5}\right)^{2}\\& = \frac{12}{25} + \frac{75}{14} + \frac{48}{125} - - \frac{75}{14} + 5 \cdot \left(- \frac{2}{5}\right)^{2}\\& = \frac{12}{25} + \frac{75}{14} + \frac{48}{125} + \frac{75}{14} + 5 \cdot \left(- \frac{2}{5}\right)^{2}\\& = \frac{12}{25} + \frac{75}{14} + \frac{48}{125} + \frac{75}{14} + 5 \cdot \frac{4}{25}\\& = \frac{12}{25} + \frac{75}{14} + \frac{48}{125} + \frac{75}{14} + \frac{4}{5}\\& = \frac{2043}{350} + \frac{48}{125} + \frac{75}{14} + \frac{4}{5}\\& = \frac{10887}{1750} + \frac{75}{14} + \frac{4}{5}\\& = \frac{10131}{875} + \frac{4}{5}\\& = \frac{10831}{875}\end{aligned}\]

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