Simplify (-(18a^2b^2)/(5cd))÷(-(9ab^3)/(5c^2d^4))

$- \frac{18 a^{2} b^{2}}{5 c d} \div (- \frac{9 a b^{3}}{5 c^{2} d^{4}})$

Step 1

To divide by a fraction, multiply by its reciprocal.

$- \frac{18 a^{2} b^{2}}{5 c d} (- \frac{5 c^{2} d^{4}}{9 a b^{3}})$

Step 2

Cancel the common factor of $9 a b^{2}$ .

Move the leading negative in $- \frac{18 a^{2} b^{2}}{5 c d}$ into the numerator.

$\frac{- 18 a^{2} b^{2}}{5 c d} (- \frac{5 c^{2} d^{4}}{9 a b^{3}})$

Move the leading negative in $- \frac{5 c^{2} d^{4}}{9 a b^{3}}$ into the numerator.

$\frac{- 18 a^{2} b^{2}}{5 c d} \cdot \frac{- 5 c^{2} d^{4}}{9 a b^{3}}$

Factor $9 a b^{2}$ out of $- 18 a^{2} b^{2}$ .

$\frac{9 a b^{2} (- 2 a)}{5 c d} \cdot \frac{- 5 c^{2} d^{4}}{9 a b^{3}}$

Factor $9 a b^{2}$ out of $9 a b^{3}$ .

$\frac{9 a b^{2} (- 2 a)}{5 c d} \cdot \frac{- 5 c^{2} d^{4}}{9 a b^{2} (b)}$

Cancel the common factor.

$\frac{9 a b^{2} (- 2 a)}{5 c d} \cdot \frac{- 5 c^{2} d^{4}}{9 a b^{2} b}$

Rewrite the expression.

$\frac{- 2 a}{5 c d} \cdot \frac{- 5 c^{2} d^{4}}{b}$

Step 3

Cancel the common factor of $5 c d$ .

Factor $5 c d$ out of $- 5 c^{2} d^{4}$ .

$\frac{- 2 a}{5 c d} \cdot \frac{5 c d (- c d^{3})}{b}$

Cancel the common factor.

$\frac{- 2 a}{5 c d} \cdot \frac{5 c d (- c d^{3})}{b}$

Rewrite the expression.

$- 2 a \frac{- c d^{3}}{b}$

Step 4

Combine $- 2$ and $\frac{- c d^{3}}{b}$ .

$a \frac{- 2 (- c d^{3})}{b}$

Step 5

Multiply $- 1$ by $- 2$ .

$a \frac{2 (c d^{3})}{b}$

Step 6

Combine $a$ and $\frac{2 (c d^{3})}{b}$ .

$\frac{a (2 (c d^{3}))}{b}$

Step 7

Move $2$ to the left of $a$ .

$\frac{2 a c d^{3}}{b}$