1. **State the problem:** Simplify the expression $$6) \frac{7}{4x^3} \cdot \frac{10x}{2x}$$. 2. **Write the expression clearly:** $$\frac{7}{4x^3} \times \frac{10x}{2x}$$. 3. **Multiply the numerators and denominators:** $$\frac{7 \times 10x}{4x^3 \times 2x} = \frac{70x}{8x^4}$$. 4. **Simplify the fraction:** Both numerator and denominator have a factor of 2 and $x$. $$\frac{\cancel{2} \times 35 \times \cancel{x}}{\cancel{2} \times 4 x^{3} \times \cancel{x}} = \frac{35}{4x^{3}}$$. 5. **Final simplified form:** $$\boxed{\frac{35}{4x^{3}}}$$. 6. **Match with options:** This corresponds to option B. **Answer:** B) $\frac{35}{4x^{3}}$