5. \( \frac{1}{3} \times \frac{22}{7} \times\left(\frac{3.5}{2}\right)^{8} \times 12 \)

To tackle the expression \( \frac{1}{3} \times \frac{22}{7} \times\left(\frac{3.5}{2}\right)^{8} \times 12 \), let's break it down step-by-step. 1. **Calculate \( \frac{3.5}{2} \)**: \[ \frac{3.5}{2} = 1.75 \] 2. **Raise \( 1.75 \) to the power of 8**: \[ (1.75)^8 \approx 24.414 \] 3. **Multiply all components together**: Now we substitute back into the expression: \[ \frac{1}{3} \times \frac{22}{7} \times 24.414 \times 12 \] 4. **Perform the multiplications**: - First multiply \( 12 \times 24.414 \): \[ 12 \times 24.414 \approx 292.968 \] - Then multiply \( \frac{22}{7} \times 292.968 \): \[ \frac{22}{7} \times 292.968 \approx 923.205 \] - Finally multiply by \( \frac{1}{3} \): \[ \frac{1}{3} \times 923.205 \approx 307.735 \] So, the approximate value of the expression is: \[ \frac{1}{3} \times \frac{22}{7} \times \left(\frac{3.5}{2}\right)^{8} \times 12 \approx 307.735 \]