Simplify ((12xy)/(z^3w))÷((20x^2y^3)/(6z^2w^4))

$\frac{12 x y}{z^{3} w} \div \frac{20 x^{2} y^{3}}{6 z^{2} w^{4}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{12 x y}{z^{3} w} \cdot \frac{6 z^{2} w^{4}}{20 x^{2} y^{3}}$

Step 2

Combine.

$\frac{12 x y (6 z^{2} w^{4})}{z^{3} w (20 x^{2} y^{3})}$

Step 3

Cancel the common factor of $12$ and $20$ .

Factor $4$ out of $12 x y (6 z^{2} w^{4})$ .

$\frac{4 (3 x y (6 z^{2} w^{4}))}{z^{3} w (20 x^{2} y^{3})}$

Cancel the common factors.

Factor $4$ out of $z^{3} w (20 x^{2} y^{3})$ .

$\frac{4 (3 x y (6 z^{2} w^{4}))}{4 (z^{3} w (5 x^{2} y^{3}))}$

Cancel the common factor.

$\frac{4 (3 x y (6 z^{2} w^{4}))}{4 (z^{3} w (5 x^{2} y^{3}))}$

Rewrite the expression.

$\frac{3 x y (6 z^{2} w^{4})}{z^{3} w (5 x^{2} y^{3})}$

Step 4

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

Factor $x$ out of $3 x y (6 z^{2} w^{4})$ .

$\frac{x (3 y (6 z^{2} w^{4}))}{z^{3} w (5 x^{2} y^{3})}$

Cancel the common factors.

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

$\frac{x (3 y (6 z^{2} w^{4}))}{x (z^{3} w (5 x y^{3}))}$

Cancel the common factor.

$\frac{x (3 y (6 z^{2} w^{4}))}{x (z^{3} w (5 x y^{3}))}$

Rewrite the expression.

$\frac{3 y (6 z^{2} w^{4})}{z^{3} w (5 x y^{3})}$

Step 5

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

Factor $y$ out of $3 y (6 z^{2} w^{4})$ .

$\frac{y (3 (6 z^{2} w^{4}))}{z^{3} w (5 x y^{3})}$

Cancel the common factors.

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

$\frac{y (3 (6 z^{2} w^{4}))}{y (z^{3} w (5 x y^{2}))}$

Cancel the common factor.

$\frac{y (3 (6 z^{2} w^{4}))}{y (z^{3} w (5 x y^{2}))}$

Rewrite the expression.

$\frac{3 (6 z^{2} w^{4})}{z^{3} w (5 x y^{2})}$

Step 6

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

Factor $z^{2}$ out of $3 (6 z^{2} w^{4})$ .

$\frac{z^{2} (3 (6 w^{4}))}{z^{3} w (5 x y^{2})}$

Cancel the common factors.

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

$\frac{z^{2} (3 (6 w^{4}))}{z^{2} (z w (5 x y^{2}))}$

Cancel the common factor.

$\frac{z^{2} (3 (6 w^{4}))}{z^{2} (z w (5 x y^{2}))}$

Rewrite the expression.

$\frac{3 (6 w^{4})}{z w (5 x y^{2})}$

Step 7

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

Factor $w$ out of $3 (6 w^{4})$ .

$\frac{w (3 (6 w^{3}))}{z w (5 x y^{2})}$

Cancel the common factors.

Factor $w$ out of $z w (5 x y^{2})$ .

$\frac{w (3 (6 w^{3}))}{w (z (5 x y^{2}))}$

Cancel the common factor.

$\frac{w (3 (6 w^{3}))}{w (z (5 x y^{2}))}$

Rewrite the expression.

$\frac{3 (6 w^{3})}{z (5 x y^{2})}$

Step 8

Simplify the expression.

Multiply $3$ by $6$ .

$\frac{18 w^{3}}{z \cdot 5 x y^{2}}$

Move $5$ to the left of $z$ .

$\frac{18 w^{3}}{5 z x y^{2}}$

Simplify ((12xy)/(z^3w))÷((20x^2y^3)/(6z^2w^4))

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