10/7 *3/4:5/14

To simplify the expression \( \frac{10}{7} \times \frac{3}{4} \div \frac{5}{14} \), we can follow these steps:

1. Rewrite the division as multiplication by the reciprocal: \[ \frac{10}{7} \times \frac{3}{4} \times \frac{14}{5} \]

2. Now, multiply the fractions together: \[ \frac{10 \times 3 \times 14}{7 \times 4 \times 5} \]

3. Calculate the numerator: \[ 10 \times 3 = 30 \] \[ 30 \times 14 = 420 \]

4. Calculate the denominator: \[ 7 \times 4 = 28 \] \[ 28 \times 5 = 140 \]

5. The expression now is: \[ \frac{420}{140} \]

6. Simplify \( \frac{420}{140} \): \[ 420 \div 140 = 3 \]

Thus, the final answer is: \[ \boxed{3} \]