Question

(dfrac{3x^{3}y^{2}sqrt{2xy}}{4x^{2}ysqrt{5y}}=)

Explanation:

Step1: Simplify rational terms

$\frac{3x^3y^2}{4x^2y} = \frac{3}{4}x^{3-2}y^{2-1} = \frac{3}{4}xy$

Step2: Simplify radical terms

$\frac{\sqrt{2xy}}{\sqrt{5y}} = \sqrt{\frac{2xy}{5y}} = \sqrt{\frac{2x}{5}}$

Step3: Combine simplified terms

$\frac{3}{4}xy \cdot \sqrt{\frac{2x}{5}} = \frac{3}{4}xy \cdot \frac{\sqrt{10x}}{5}$

Step4: Final coefficient simplification

$\frac{3}{4} \cdot \frac{1}{5}xy\sqrt{10x} = \frac{3}{20}xy\sqrt{10x}$

Answer:

$\frac{3}{20}xy\sqrt{10x}$