How do you multiply $\frac{2 x^{4}}{10 y^{2}} \cdot \frac{5 y^{3}}{4 x^{3}}$ $(2x^4)/ (10y^2) * ( 5y^3)/(4x^3)$ ?

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Answer 1 · 2015-06-08T00:00:06

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

I simplify "in cross" the two cohefficients:

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

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

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

$\frac{x^{4} y^{3}}{2 x^{3} y^{2}}$ $(x^4y^3)/(2x^3y^2)$

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

$\frac{x^{4 - 3} \cdot y^{3 - 2}}{2 \cdot x^{3 - 3} \cdot y^{2 - 2}}$ $(x^(4-3)*y^(3-2))/(2*x^(3-3)*y^(2-2))$

That is basically:

$\frac{x y}{2}$ $(xy)/2$

How do you multiply (2x^4)/ (10y^2) * ( 5y^3)/(4x^3)2x410y2⋅5y34x3 (2x^4)/ (10y^2) * ( 5y^3)/(4x^3)?