2*2*2*2+(16-3*4)/(6+3*3)/(7-4)

asked by guest
on Jan 23, 2025 at 8:43 am



You asked:

Evaluate the expression: \(2 \cdot 2 \cdot 2 \cdot 2 + \frac{\frac{16 - 3 \cdot 4}{6 + 3 \cdot 3}}{7 - 4}\)

MathBot Answer:

\[2 \cdot 2 \cdot 2 \cdot 2 + \frac{\frac{16 - 3 \cdot 4}{6 + 3 \cdot 3}}{7 - 4} = \frac{724}{45} = 16.0\overline{8}\]

\[\begin{aligned}2 \cdot 2 \cdot 2 \cdot 2 + \frac{\frac{16 - 3 \cdot 4}{6 + 3 \cdot 3}}{7 - 4}& = 2 \cdot 2 \cdot 2 \cdot 2 + \left(16 - 3 \cdot 4\right) \cdot \frac{1}{6 + 3 \cdot 3} \cdot \frac{1}{7 - 4}\\& = 4 \cdot 2 \cdot 2 + \left(16 - 3 \cdot 4\right) \cdot \frac{1}{6 + 3 \cdot 3} \cdot \frac{1}{7 - 4}\\& = 8 \cdot 2 + \left(16 - 3 \cdot 4\right) \cdot \frac{1}{6 + 3 \cdot 3} \cdot \frac{1}{7 - 4}\\& = 16 + \left(16 - 3 \cdot 4\right) \cdot \frac{1}{6 + 3 \cdot 3} \cdot \frac{1}{7 - 4}\\& = 16 + \left(16 - 12\right) \cdot \frac{1}{6 + 3 \cdot 3} \cdot \frac{1}{7 - 4}\\& = 16 + 4 \cdot \frac{1}{6 + 3 \cdot 3} \cdot \frac{1}{7 - 4}\\& = 16 + 4 \cdot \frac{1}{6 + 9} \cdot \frac{1}{7 - 4}\\& = 16 + \frac{4}{15} \cdot \frac{1}{7 - 4}\\& = 16 + \frac{4}{15} \cdot \frac{1}{3}\\& = 16 + \frac{4}{45}\\& = \frac{724}{45}\end{aligned}\]

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