Simplify (2x^4)/(10y^2)*(5y^3)/(4x^3)

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

Step 1

Combine.

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

Step 2

Cancel the common factor of $2$ and $10$ .

Factor $2$ out of $2 x^{4} (5 y^{3})$ .

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

Cancel the common factors.

Factor $2$ out of $10 y^{2} (4 x^{3})$ .

$\frac{2 (x^{4} (5 y^{3}))}{2 (5 y^{2} (4 x^{3}))}$

Cancel the common factor.

$\frac{2 (x^{4} (5 y^{3}))}{2 (5 y^{2} (4 x^{3}))}$

Rewrite the expression.

$\frac{x^{4} (5 y^{3})}{5 y^{2} (4 x^{3})}$

Step 3

Cancel the common factor of $x^{4}$ and $x^{3}$ .

Factor $x^{3}$ out of $x^{4} (5 y^{3})$ .

$\frac{x^{3} (x (5 y^{3}))}{5 y^{2} (4 x^{3})}$

Cancel the common factors.

Factor $x^{3}$ out of $5 y^{2} (4 x^{3})$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Cancel the common factor of $5$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 5

Cancel the common factor of $y^{3}$ and $y^{2}$ .

Factor $y^{2}$ out of $x (y^{3})$ .

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

Cancel the common factors.

Factor $y^{2}$ out of $y^{2} \cdot (4)$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{x (y)}{4}$

$\frac{x y}{4}$