# How do you multiply  (2x^4)/ (10y^2) * ( 5y^3)/(4x^3)?

Jun 8, 2015

$\frac{2 {x}^{4}}{10 {y}^{2}} \cdot \frac{5 {y}^{3}}{4 {x}^{3}}$

I simplify "in cross" the two cohefficients:

$\frac{2 {x}^{4}}{2 {y}^{2}} \cdot \frac{{y}^{3}}{4 {x}^{3}}$ (simplified 10 and 5)

$\frac{{x}^{4}}{{y}^{2}} \cdot \frac{{y}^{3}}{2 {x}^{3}}$ (simplified 4 and 2)

Now I multiply the variables together and I order them to work properly:

$\frac{{x}^{4} {y}^{3}}{2 {x}^{3} {y}^{2}}$

Assuming that $x \ne 0$ and $y \ne 0$, I can reduce the degree of the variables in this way:

$\frac{{x}^{4 - 3} \cdot {y}^{3 - 2}}{2 \cdot {x}^{3 - 3} \cdot {y}^{2 - 2}}$

That is basically:

$\frac{x y}{2}$