Divide (-120m^4n^6-32m^2n^3)/(8m^2n^2)

$\frac{- 120 m^{4} n^{6} - 32 m^{2} n^{3}}{8 m^{2} n^{2}}$

Step 1

Factor $8 m^{2} n^{3}$ out of $- 120 m^{4} n^{6} - 32 m^{2} n^{3}$ .

Factor $8 m^{2} n^{3}$ out of $- 120 m^{4} n^{6}$ .

$\frac{8 m^{2} n^{3} (- 15 m^{2} n^{3}) - 32 m^{2} n^{3}}{8 m^{2} n^{2}}$

Factor $8 m^{2} n^{3}$ out of $- 32 m^{2} n^{3}$ .

$\frac{8 m^{2} n^{3} (- 15 m^{2} n^{3}) + 8 m^{2} n^{3} (- 4)}{8 m^{2} n^{2}}$

Factor $8 m^{2} n^{3}$ out of $8 m^{2} n^{3} (- 15 m^{2} n^{3}) + 8 m^{2} n^{3} (- 4)$ .

$\frac{8 m^{2} n^{3} (- 15 m^{2} n^{3} - 4)}{8 m^{2} n^{2}}$

Step 2

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 m^{2} n^{3} (- 15 m^{2} n^{3} - 4)}{8 m^{2} n^{2}}$

Rewrite the expression.

$\frac{m^{2} n^{3} (- 15 m^{2} n^{3} - 4)}{m^{2} n^{2}}$

Step 3

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

Cancel the common factor.

$\frac{m^{2} n^{3} (- 15 m^{2} n^{3} - 4)}{m^{2} n^{2}}$

Rewrite the expression.

$\frac{n^{3} (- 15 m^{2} n^{3} - 4)}{n^{2}}$

Step 4

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

Factor $n^{2}$ out of $n^{3} (- 15 m^{2} n^{3} - 4)$ .

$\frac{n^{2} (n (- 15 m^{2} n^{3} - 4))}{n^{2}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{n^{2} (n (- 15 m^{2} n^{3} - 4))}{n^{2} \cdot 1}$

Cancel the common factor.

$\frac{n^{2} (n (- 15 m^{2} n^{3} - 4))}{n^{2} \cdot 1}$

Rewrite the expression.

$\frac{n (- 15 m^{2} n^{3} - 4)}{1}$

Divide $n (- 15 m^{2} n^{3} - 4)$ by $1$ .

$n (- 15 m^{2} n^{3} - 4)$

Step 5

Apply the distributive property.

$n (- 15 m^{2} n^{3}) + n \cdot - 4$

Step 6

Rewrite using the commutative property of multiplication.

$- 15 n (m^{2} n^{3}) + n \cdot - 4$

Step 7

Move $- 4$ to the left of $n$ .

$- 15 n (m^{2} n^{3}) - 4 \cdot n$

Step 8

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

Move $n^{3}$ .

$- 15 (n^{3} n) m^{2} - 4 \cdot n$

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

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

$- 15 (n^{3} n^{1}) m^{2} - 4 \cdot n$

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

$- 15 n^{3 + 1} m^{2} - 4 \cdot n$

Add $3$ and $1$ .

$- 15 n^{4} m^{2} - 4 \cdot n$

$- 15 n^{4} m^{2} - 4 n$

Divide (-120m^4n^6-32m^2n^3)/(8m^2n^2)

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