1. **State the problem:** We are given the area and length of a rectangle and need to find an expression for its width. 2. **Recall the formula for the area of a rectangle:** $$\text{Area} = \text{Length} \times \text{Width}$$ 3. **Given:** $$\text{Area} = \frac{5 x^3 y^4}{3 p q}$$ $$\text{Length} = \frac{4 x y}{p}$$ 4. **Find width by rearranging the area formula:** $$\text{Width} = \frac{\text{Area}}{\text{Length}}$$ 5. **Substitute the given expressions:** $$\text{Width} = \frac{\frac{5 x^3 y^4}{3 p q}}{\frac{4 x y}{p}}$$ 6. **Simplify the complex fraction:** $$\text{Width} = \frac{5 x^3 y^4}{3 p q} \times \frac{p}{4 x y}$$ 7. **Multiply numerators and denominators:** $$\text{Width} = \frac{5 x^3 y^4 \times p}{3 p q \times 4 x y} = \frac{5 p x^3 y^4}{12 p q x y}$$ 8. **Cancel common factors:** - Cancel $p$ from numerator and denominator. - Cancel $x$ from $x^3$ and $x$ leaving $x^{3-1} = x^2$. - Cancel $y$ from $y^4$ and $y$ leaving $y^{4-1} = y^3$. So, $$\text{Width} = \frac{5 x^2 y^3}{12 q}$$ **Final answer:** $$\boxed{\frac{5 x^2 y^3}{12 q}}$$