Simplify (-(9y^2)/(20x^3))÷((y^5)/(16x))

$- \frac{9 y^{2}}{20 x^{3}} \div \frac{y^{5}}{16 x}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$- \frac{9 y^{2}}{20 x^{3}} \cdot \frac{16 x}{y^{5}}$

Step 2

Cancel the common factor of $y^{2}$ .

Move the leading negative in $- \frac{9 y^{2}}{20 x^{3}}$ into the numerator.

$\frac{- 9 y^{2}}{20 x^{3}} \cdot \frac{16 x}{y^{5}}$

Factor $y^{2}$ out of $- 9 y^{2}$ .

$\frac{y^{2} \cdot - 9}{20 x^{3}} \cdot \frac{16 x}{y^{5}}$

Factor $y^{2}$ out of $y^{5}$ .

$\frac{y^{2} \cdot - 9}{20 x^{3}} \cdot \frac{16 x}{y^{2} y^{3}}$

Cancel the common factor.

$\frac{y^{2} \cdot - 9}{20 x^{3}} \cdot \frac{16 x}{y^{2} y^{3}}$

Rewrite the expression.

$\frac{- 9}{20 x^{3}} \cdot \frac{16 x}{y^{3}}$

Step 3

Cancel the common factor of $4 x$ .

Factor $4 x$ out of $20 x^{3}$ .

$\frac{- 9}{4 x (5 x^{2})} \cdot \frac{16 x}{y^{3}}$

Factor $4 x$ out of $16 x$ .

$\frac{- 9}{4 x (5 x^{2})} \cdot \frac{4 x (4)}{y^{3}}$

Cancel the common factor.

$\frac{- 9}{4 x (5 x^{2})} \cdot \frac{4 x \cdot 4}{y^{3}}$

Rewrite the expression.

$\frac{- 9}{5 x^{2}} \cdot \frac{4}{y^{3}}$

Step 4

Multiply $\frac{- 9}{5 x^{2}}$ by $\frac{4}{y^{3}}$ .

$\frac{- 9 \cdot 4}{5 x^{2} y^{3}}$

Step 5

Simplify the expression.

Multiply $- 9$ by $4$ .

$\frac{- 36}{5 x^{2} y^{3}}$

Move the negative in front of the fraction.

$- \frac{36}{5 x^{2} y^{3}}$