Simplify (1/(9x^2))÷(3/(2x))

$\frac{1}{9 x^{2}} \div \frac{3}{2 x}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{1}{9 x^{2}} \cdot \frac{2 x}{3}$

Step 2

Simplify terms.

Combine.

$\frac{1 (2 x)}{9 x^{2} \cdot 3}$

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

Factor $x$ out of $1 (2 x)$ .

$\frac{x (1 \cdot (2))}{9 x^{2} \cdot 3}$

Cancel the common factors.

Factor $x$ out of $9 x^{2} \cdot 3$ .

$\frac{x (1 \cdot (2))}{x (9 x \cdot 3)}$

Cancel the common factor.

$\frac{x (1 \cdot (2))}{x (9 x \cdot 3)}$

Rewrite the expression.

$\frac{1 \cdot (2)}{9 x \cdot 3}$

Step 3

Multiply $2$ by $1$ .

$\frac{2}{9 x \cdot 3}$

Step 4

Multiply $3$ by $9$ .

$\frac{2}{27 x}$