2/3*22/7*1.4*1.4*1.4

asked by guest
on Dec 08, 2024 at 4:46 am



You asked:

Evaluate the expression: \(\frac{\frac{2}{3} \cdot 22}{7} \cdot 1.4 \cdot 1.4 \cdot 1.4\)

MathBot Answer:

\[\frac{\frac{2}{3} \cdot 22}{7} \cdot 1.4 \cdot 1.4 \cdot 1.4 = \frac{2156}{375} = 5.749\overline{3}\]

\[\begin{aligned}\frac{\frac{2}{3} \cdot 22}{7} \cdot 1.4 \cdot 1.4 \cdot 1.4& = \frac{2}{3} \cdot \frac{22}{7} \cdot \left(1 + \frac{4}{10}\right) \cdot \left(1 + \frac{4}{10}\right) \cdot \left(1 + \frac{4}{10}\right)\\& = \frac{2}{3} \cdot \frac{22}{7} \cdot \left(1 + \frac{2}{5}\right) \cdot \left(1 + \frac{4}{10}\right) \cdot \left(1 + \frac{4}{10}\right)\\& = \frac{2}{3} \cdot \frac{22}{7} \cdot \frac{7}{5} \cdot \left(1 + \frac{4}{10}\right) \cdot \left(1 + \frac{4}{10}\right)\\& = \frac{2}{3} \cdot \frac{22}{7} \cdot \frac{7}{5} \cdot \left(1 + \frac{2}{5}\right) \cdot \left(1 + \frac{4}{10}\right)\\& = \frac{2}{3} \cdot \frac{22}{7} \cdot \frac{7}{5} \cdot \frac{7}{5} \cdot \left(1 + \frac{4}{10}\right)\\& = \frac{2}{3} \cdot \frac{22}{7} \cdot \frac{7}{5} \cdot \frac{7}{5} \cdot \left(1 + \frac{2}{5}\right)\\& = \frac{2}{3} \cdot \frac{22}{7} \cdot \frac{7}{5} \cdot \frac{7}{5} \cdot \frac{7}{5}\\& = \frac{44}{3} \cdot \frac{1}{7} \cdot \frac{7}{5} \cdot \frac{7}{5} \cdot \frac{7}{5}\\& = \frac{44}{21} \cdot \frac{7}{5} \cdot \frac{7}{5} \cdot \frac{7}{5}\\& = \frac{44}{15} \cdot \frac{7}{5} \cdot \frac{7}{5}\\& = \frac{308}{75} \cdot \frac{7}{5}\\& = \frac{2156}{375}\end{aligned}\]

+ Submit Question