Math Problem Solver

\[-6 \cdot \left(\frac{1}{3} - \frac{1}{2} - \left(\frac{{0.4}^{3}}{3} - \frac{{0.4}^{2}}{2}\right)\right) = \frac{81}{125} = 0.648\]

\[\begin{aligned}-6 \cdot \left(\frac{1}{3} - \frac{1}{2} - \left(\frac{{0.4}^{3}}{3} - \frac{{0.4}^{2}}{2}\right)\right)& = -6 \cdot \left(\frac{1}{3} - \frac{1}{2} - \left(\left(\frac{4}{10}\right)^{3} \cdot \frac{1}{3} - \left(\frac{4}{10}\right)^{2} \cdot \frac{1}{2}\right)\right)\\& = -6 \cdot \left(\frac{1}{3} - \frac{1}{2} - \left(\left(\frac{2}{5}\right)^{3} \cdot \frac{1}{3} - \left(\frac{4}{10}\right)^{2} \cdot \frac{1}{2}\right)\right)\\& = -6 \cdot \left(\frac{1}{3} - \frac{1}{2} - \left(\frac{8}{125} \cdot \frac{1}{3} - \left(\frac{4}{10}\right)^{2} \cdot \frac{1}{2}\right)\right)\\& = -6 \cdot \left(\frac{1}{3} - \frac{1}{2} - \left(\frac{8}{375} - \left(\frac{4}{10}\right)^{2} \cdot \frac{1}{2}\right)\right)\\& = -6 \cdot \left(\frac{1}{3} - \frac{1}{2} - \left(\frac{8}{375} - \left(\frac{2}{5}\right)^{2} \cdot \frac{1}{2}\right)\right)\\& = -6 \cdot \left(\frac{1}{3} - \frac{1}{2} - \left(\frac{8}{375} - \frac{4}{25} \cdot \frac{1}{2}\right)\right)\\& = -6 \cdot \left(\frac{1}{3} - \frac{1}{2} - \left(\frac{8}{375} - \frac{2}{25}\right)\right)\\& = -6 \cdot \left(\frac{1}{3} - \frac{1}{2} - - \frac{22}{375}\right)\\& = -6 \cdot \left(\frac{1}{3} - \frac{1}{2} + \frac{22}{375}\right)\\& = -6 \cdot \left(- \frac{1}{6} + \frac{22}{375}\right)\\& = -6 \cdot - \frac{27}{250}\\& = \frac{81}{125}\end{aligned}\]