1. **State the problem:** Calculate the value of the expression $10 \times 7 \times \left(8 \div 40\right) \times 7 \times 2$. 2. **Recall the order of operations:** Perform operations inside parentheses first, then multiplication and division from left to right. 3. **Calculate inside the parentheses:** $$8 \div 40 = \frac{8}{40}$$ Simplify the fraction by canceling common factors: $$\frac{\cancel{8}}{\cancel{40}} = \frac{1}{5}$$ 4. **Rewrite the expression:** $$10 \times 7 \times \frac{1}{5} \times 7 \times 2$$ 5. **Multiply step-by-step:** $$10 \times 7 = 70$$ $$70 \times \frac{1}{5} = \frac{70}{5}$$ Simplify by canceling common factors: $$\frac{\cancel{70}}{\cancel{5}} = 14$$ 6. **Continue multiplying:** $$14 \times 7 = 98$$ $$98 \times 2 = 196$$ 7. **Final answer:** $$196$$