Simplify 1/4(8mn)*(-6m^2n^2)

$\frac{1}{4} (8 m n) \cdot (- 6 m^{2} n^{2})$

Step 1

Multiply $m$ by $m^{2}$ by adding the exponents.

Move $m^{2}$ .

$\frac{1}{4} \cdot (8 (m^{2} m) n) \cdot (- 6 n^{2})$

Multiply $m^{2}$ by $m$ .

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

$\frac{1}{4} \cdot (8 (m^{2} m^{1}) n) \cdot (- 6 n^{2})$

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

$\frac{1}{4} \cdot (8 m^{2 + 1} n) \cdot (- 6 n^{2})$

Add $2$ and $1$ .

$\frac{1}{4} \cdot (8 m^{3} n) \cdot (- 6 n^{2})$

Step 2

Multiply $n$ by $n^{2}$ by adding the exponents.

Move $n^{2}$ .

$\frac{1}{4} \cdot (8 m^{3} (n^{2} n)) \cdot - 6$

Multiply $n^{2}$ by $n$ .

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

$\frac{1}{4} \cdot (8 m^{3} (n^{2} n^{1})) \cdot - 6$

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

$\frac{1}{4} \cdot (8 m^{3} n^{2 + 1}) \cdot - 6$

Add $2$ and $1$ .

$\frac{1}{4} \cdot (8 m^{3} n^{3}) \cdot - 6$

Step 3

Cancel the common factor of $4$ .

Factor $4$ out of $8 m^{3} n^{3}$ .

$\frac{1}{4} \cdot (4 (2 m^{3} n^{3})) \cdot - 6$

Cancel the common factor.

$\frac{1}{4} \cdot (4 (2 m^{3} n^{3})) \cdot - 6$

Rewrite the expression.

$2 m^{3} n^{3} \cdot - 6$

Step 4

Multiply $- 6$ by $2$ .

$- 12 m^{3} n^{3}$