Simplify ((18xy^3)/(5a^2b))÷((6x^2y)/(20ab))

$\frac{18 x y^{3}}{5 a^{2} b} \div \frac{6 x^{2} y}{20 a b}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{18 x y^{3}}{5 a^{2} b} \cdot \frac{20 a b}{6 x^{2} y}$

Step 2

Combine.

$\frac{18 x y^{3} (20 a b)}{5 a^{2} b (6 x^{2} y)}$

Step 3

Cancel the common factor of $18$ and $6$ .

Factor $6$ out of $18 x y^{3} (20 a b)$ .

$\frac{6 (3 x y^{3} (20 a b))}{5 a^{2} b (6 x^{2} y)}$

Cancel the common factors.

Factor $6$ out of $5 a^{2} b (6 x^{2} y)$ .

$\frac{6 (3 x y^{3} (20 a b))}{6 (5 a^{2} b (x^{2} y))}$

Cancel the common factor.

$\frac{6 (3 x y^{3} (20 a b))}{6 (5 a^{2} b (x^{2} y))}$

Rewrite the expression.

$\frac{3 x y^{3} (20 a b)}{5 a^{2} b (x^{2} y)}$

Step 4

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

Factor $x$ out of $3 x y^{3} (20 a b)$ .

$\frac{x (3 y^{3} (20 a b))}{5 a^{2} b (x^{2} y)}$

Cancel the common factors.

Factor $x$ out of $5 a^{2} b (x^{2} y)$ .

$\frac{x (3 y^{3} (20 a b))}{x (5 a^{2} b (x y))}$

Cancel the common factor.

$\frac{x (3 y^{3} (20 a b))}{x (5 a^{2} b (x y))}$

Rewrite the expression.

$\frac{3 y^{3} (20 a b)}{5 a^{2} b (x y)}$

Step 5

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

Factor $y$ out of $3 y^{3} (20 a b)$ .

$\frac{y (3 y^{2} (20 a b))}{5 a^{2} b (x y)}$

Cancel the common factors.

Factor $y$ out of $5 a^{2} b (x y)$ .

$\frac{y (3 y^{2} (20 a b))}{y (5 a^{2} b (x))}$

Cancel the common factor.

$\frac{y (3 y^{2} (20 a b))}{y (5 a^{2} b (x))}$

Rewrite the expression.

$\frac{3 y^{2} (20 a b)}{5 a^{2} b (x)}$

Step 6

Cancel the common factor of $20$ and $5$ .

Factor $5$ out of $3 y^{2} (20 a b)$ .

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

Cancel the common factors.

Factor $5$ out of $5 a^{2} b (x)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 7

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

Factor $a$ out of $3 y^{2} (4 a b)$ .

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

Cancel the common factors.

Factor $a$ out of $a^{2} b (x)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 8

Cancel the common factor of $b$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 9

Multiply $4$ by $3$ .

$\frac{12 y^{2}}{a x}$

Simplify ((18xy^3)/(5a^2b))÷((6x^2y)/(20ab))

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