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

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

To divide by a fraction, multiply by its reciprocal.

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

Combine.

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

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

Factor $6$ out of $18 x^{2} y (20 a^{2} b)$ .

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

Cancel the common factors.

Factor $6$ out of $5 a b (6 x y^{3})$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $b$ .

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $4$ by $3$ .

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

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

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