Simplify (3x^2y^2*4x^3y^3)÷(-2xy^4)

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

Step 1

Rewrite the division as a fraction.

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

Step 2

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

Move $x^{3}$ .

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

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

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

Add $3$ and $2$ .

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

Step 3

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

Move $y^{3}$ .

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

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

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

Add $3$ and $2$ .

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

Step 4

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 5

Cancel the common factor of $y^{5}$ and $y^{4}$ .

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 6

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

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

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

Move the negative one from the denominator of $\frac{3 x^{4} y \cdot 2}{- 1}$ .

$- 1 \cdot (3 x^{4} y \cdot 2)$

Step 7

Simplify the expression.

Rewrite $- 1 \cdot (3 x^{4} y \cdot 2)$ as $- (3 x^{4} y \cdot 2)$ .

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

Multiply $2$ by $3$ .

$- (6 x^{4} y)$

Multiply $6$ by $- 1$ .

$- 6 x^{4} y$

Simplify (3x^2y^2*4x^3y^3)÷(-2xy^4)

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