Math Problem Solver

\[3.14 \cdot \left(8 + \frac{4}{3} \cdot 4.25 \cdot 4.25 \cdot 4.25\right) = \frac{831629}{2400} = 346.51208\overline{3}\]

\[\begin{aligned}3.14 \cdot \left(8 + \frac{4}{3} \cdot 4.25 \cdot 4.25 \cdot 4.25\right)& = \left(3 + \frac{14}{100}\right) \cdot \left(8 + \frac{4}{3} \cdot \left(4 + \frac{25}{100}\right) \cdot \left(4 + \frac{25}{100}\right) \cdot \left(4 + \frac{25}{100}\right)\right)\\& = \left(3 + \frac{7}{50}\right) \cdot \left(8 + \frac{4}{3} \cdot \left(4 + \frac{25}{100}\right) \cdot \left(4 + \frac{25}{100}\right) \cdot \left(4 + \frac{25}{100}\right)\right)\\& = \frac{157}{50} \cdot \left(8 + \frac{4}{3} \cdot \left(4 + \frac{25}{100}\right) \cdot \left(4 + \frac{25}{100}\right) \cdot \left(4 + \frac{25}{100}\right)\right)\\& = \frac{157}{50} \cdot \left(8 + \frac{4}{3} \cdot \left(4 + \frac{1}{4}\right) \cdot \left(4 + \frac{25}{100}\right) \cdot \left(4 + \frac{25}{100}\right)\right)\\& = \frac{157}{50} \cdot \left(8 + \frac{4}{3} \cdot \frac{17}{4} \cdot \left(4 + \frac{25}{100}\right) \cdot \left(4 + \frac{25}{100}\right)\right)\\& = \frac{157}{50} \cdot \left(8 + \frac{4}{3} \cdot \frac{17}{4} \cdot \left(4 + \frac{1}{4}\right) \cdot \left(4 + \frac{25}{100}\right)\right)\\& = \frac{157}{50} \cdot \left(8 + \frac{4}{3} \cdot \frac{17}{4} \cdot \frac{17}{4} \cdot \left(4 + \frac{25}{100}\right)\right)\\& = \frac{157}{50} \cdot \left(8 + \frac{4}{3} \cdot \frac{17}{4} \cdot \frac{17}{4} \cdot \left(4 + \frac{1}{4}\right)\right)\\& = \frac{157}{50} \cdot \left(8 + \frac{4}{3} \cdot \frac{17}{4} \cdot \frac{17}{4} \cdot \frac{17}{4}\right)\\& = \frac{157}{50} \cdot \left(8 + \frac{17}{3} \cdot \frac{17}{4} \cdot \frac{17}{4}\right)\\& = \frac{157}{50} \cdot \left(8 + \frac{289}{12} \cdot \frac{17}{4}\right)\\& = \frac{157}{50} \cdot \left(8 + \frac{4913}{48}\right)\\& = \frac{157}{50} \cdot \frac{5297}{48}\\& = \frac{831629}{2400}\end{aligned}\]