Simplify (14/(9x^3))÷((7x)/(2y^2))

$\frac{14}{9 x^{3}} \div \frac{7 x}{2 y^{2}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{14}{9 x^{3}} \cdot \frac{2 y^{2}}{7 x}$

Step 2

Combine.

$\frac{14 (2 y^{2})}{9 x^{3} (7 x)}$

Step 3

Multiply $x^{3}$ by $x$ by adding the exponents.

Move $x$ .

$\frac{14 (2 y^{2})}{9 (x \cdot x^{3}) \cdot 7}$

Multiply $x$ by $x^{3}$ .

Raise $x$ to the power of $1$ .

$\frac{14 (2 y^{2})}{9 (x^{1} x^{3}) \cdot 7}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{14 (2 y^{2})}{9 x^{1 + 3} \cdot 7}$

Add $1$ and $3$ .

$\frac{14 (2 y^{2})}{9 x^{4} \cdot 7}$

Step 4

Cancel the common factor of $14$ and $7$ .

Factor $7$ out of $14 (2 y^{2})$ .

$\frac{7 (2 (2 y^{2}))}{9 x^{4} \cdot 7}$

Cancel the common factors.

Factor $7$ out of $9 x^{4} \cdot 7$ .

$\frac{7 (2 (2 y^{2}))}{7 \cdot (9 x^{4})}$

Cancel the common factor.

$\frac{7 (2 (2 y^{2}))}{7 \cdot (9 x^{4})}$

Rewrite the expression.

$\frac{2 (2 y^{2})}{9 x^{4}}$

Step 5

Simplify the expression.

Multiply $2$ by $2$ .

$\frac{2^{2} y^{2}}{9 x^{4}}$

Raise $2$ to the power of $2$ .

$\frac{4 y^{2}}{9 x^{4}}$