Simplify ((-25/(18m))(-(27n)/(6m)))÷(-n/(4mn))

$(- \frac{25}{18 m}) (- \frac{27 n}{6 m}) \div (- \frac{n}{4 m n})$

Step 1

To divide by a fraction, multiply by its reciprocal.

$(- \frac{25}{18 m}) (- \frac{27 n}{6 m}) (- \frac{4 m n}{n})$

Step 2

Cancel the common factor of $9$ .

Move the leading negative in $- \frac{25}{18 m}$ into the numerator.

$\frac{- 25}{18 m} (- \frac{27 n}{6 m}) (- \frac{4 m n}{n})$

Move the leading negative in $- \frac{27 n}{6 m}$ into the numerator.

$\frac{- 25}{18 m} \cdot \frac{- 27 n}{6 m} (- \frac{4 m n}{n})$

Factor $9$ out of $18 m$ .

$\frac{- 25}{9 (2 m)} \cdot \frac{- 27 n}{6 m} (- \frac{4 m n}{n})$

Factor $9$ out of $- 27 n$ .

$\frac{- 25}{9 (2 m)} \cdot \frac{9 (- 3 n)}{6 m} (- \frac{4 m n}{n})$

Cancel the common factor.

$\frac{- 25}{9 (2 m)} \cdot \frac{9 (- 3 n)}{6 m} (- \frac{4 m n}{n})$

Rewrite the expression.

$\frac{- 25}{2 m} \cdot \frac{- 3 n}{6 m} (- \frac{4 m n}{n})$

Step 3

Multiply $\frac{- 25}{2 m}$ by $\frac{- 3 n}{6 m}$ .

$\frac{- 25 (- 3 n)}{2 m (6 m)} (- \frac{4 m n}{n})$

Step 4

Multiply.

Multiply $- 3$ by $- 25$ .

$\frac{75 n}{2 m (6 m)} (- \frac{4 m n}{n})$

Multiply $6$ by $2$ .

$\frac{75 n}{12 m \cdot m} (- \frac{4 m n}{n})$

Step 5

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

$\frac{75 n}{12 (m^{1} m)} (- \frac{4 m n}{n})$

Step 6

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

$\frac{75 n}{12 (m^{1} m^{1})} (- \frac{4 m n}{n})$

Step 7

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

$\frac{75 n}{12 m^{1 + 1}} (- \frac{4 m n}{n})$

Step 8

Simplify the expression.

Add $1$ and $1$ .

$\frac{75 n}{12 m^{2}} (- \frac{4 m n}{n})$

Rewrite using the commutative property of multiplication.

$- \frac{75 n}{12 m^{2}} \cdot \frac{4 m n}{n}$

Step 9

Cancel the common factor of $n$ .

Move the leading negative in $- \frac{75 n}{12 m^{2}}$ into the numerator.

$\frac{- 75 n}{12 m^{2}} \cdot \frac{4 m n}{n}$

Factor $n$ out of $- 75 n$ .

$\frac{n \cdot - 75}{12 m^{2}} \cdot \frac{4 m n}{n}$

Cancel the common factor.

$\frac{n \cdot - 75}{12 m^{2}} \cdot \frac{4 m n}{n}$

Rewrite the expression.

$\frac{- 75}{12 m^{2}} (4 m n)$

Step 10

Cancel the common factor of $4 m$ .

Factor $4 m$ out of $12 m^{2}$ .

$\frac{- 75}{4 m (3 m)} (4 m n)$

Factor $4 m$ out of $4 m n$ .

$\frac{- 75}{4 m (3 m)} (4 m (n))$

Cancel the common factor.

$\frac{- 75}{4 m (3 m)} (4 m n)$

Rewrite the expression.

$\frac{- 75}{3 m} n$

Step 11

Combine $\frac{- 75}{3 m}$ and $n$ .

$\frac{- 75 n}{3 m}$

Step 12

Cancel the common factor of $- 75$ and $3$ .

Factor $3$ out of $- 75 n$ .

$\frac{3 (- 25 n)}{3 m}$

Cancel the common factors.

Factor $3$ out of $3 m$ .

$\frac{3 (- 25 n)}{3 (m)}$

Cancel the common factor.

$\frac{3 (- 25 n)}{3 m}$

Rewrite the expression.

$\frac{- 25 n}{m}$

Step 13

Move the negative in front of the fraction.

$- \frac{25 n}{m}$

Simplify ((-25/(18m))(-(27n)/(6m)))÷(-n/(4mn))

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