Simplify (1/(2x^3))÷(9/(7x^2))

$\frac{1}{2 x^{3}} \div \frac{9}{7 x^{2}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{1}{2 x^{3}} \cdot \frac{7 x^{2}}{9}$

Step 2

Simplify terms.

Combine.

$\frac{1 (7 x^{2})}{2 x^{3} \cdot 9}$

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

Factor $x^{2}$ out of $1 (7 x^{2})$ .

$\frac{x^{2} (1 \cdot (7))}{2 x^{3} \cdot 9}$

Cancel the common factors.

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

$\frac{x^{2} (1 \cdot (7))}{x^{2} (2 x \cdot 9)}$

Cancel the common factor.

$\frac{x^{2} (1 \cdot (7))}{x^{2} (2 x \cdot 9)}$

Rewrite the expression.

$\frac{1 \cdot (7)}{2 x \cdot 9}$

Step 3

Multiply $7$ by $1$ .

$\frac{7}{2 x \cdot 9}$

Step 4

Multiply $9$ by $2$ .

$\frac{7}{18 x}$