Simplify (-4x^3*x^2y^4)/(-2x^3y^4)

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

Step 1

Multiply $x^{3}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $2$ and $3$ .

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

Step 2

Cancel the common factor of $- 4$ and $- 2$ .

Factor $- 2$ out of $- 4 x^{5} \cdot y^{4}$ .

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

Cancel the common factors.

Factor $- 2$ out of $- 2 x^{3} y^{4}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Cancel the common factor of $x^{5}$ and $x^{3}$ .

Factor $x^{3}$ out of $2 x^{5} \cdot y^{4}$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Cancel the common factor of $y^{4}$ .

Cancel the common factor.

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

Divide $2 x^{2}$ by $1$ .

$2 x^{2}$