Algebra Examples

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

Step 1

Cancel the common factor of $2$ .

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Step 1.1

Factor $2$ out of $4$ .

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

Step 1.2

Factor $2$ out of $(8 m n) (- 6 m^{2} n^{2})$ .

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

Step 1.3

Cancel the common factor.

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

Step 1.4

Rewrite the expression.

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

Step 2

Multiply $- 6$ by $4$ .

$\frac{1}{2} \cdot (- 24 m n (m^{2} n^{2}))$

Step 3

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

$\frac{1}{2} \cdot (- 24 (m^{2} m^{1}) n \cdot n^{2})$

Step 4

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

$\frac{1}{2} \cdot (- 24 m^{2 + 1} n \cdot n^{2})$

Step 5

Add $2$ and $1$ .

$\frac{1}{2} \cdot (- 24 m^{3} n \cdot n^{2})$

Step 6

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

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Step 6.1

Move $n^{2}$ .

$\frac{1}{2} \cdot (- 24 m^{3} (n^{2} n))$

Step 6.2

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

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Step 6.2.1

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

$\frac{1}{2} \cdot (- 24 m^{3} (n^{2} n^{1}))$

Step 6.2.2

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

$\frac{1}{2} \cdot (- 24 m^{3} n^{2 + 1})$

Step 6.3

Add $2$ and $1$ .

$\frac{1}{2} \cdot (- 24 m^{3} n^{3})$

Step 7

Combine $- 24$ and $\frac{1}{2}$ .

$\frac{- 24}{2} \cdot (m^{3} n^{3})$

Step 8

Combine $m^{3}$ and $\frac{- 24}{2}$ .

$\frac{m^{3} \cdot - 24}{2} \cdot n^{3}$

Step 9

Combine $\frac{m^{3} \cdot - 24}{2}$ and $n^{3}$ .

$\frac{m^{3} \cdot - 24 n^{3}}{2}$

Step 10

Cancel the common factor of $- 24$ and $2$ .

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Step 10.1

Factor $2$ out of $m^{3} \cdot - 24 n^{3}$ .

$\frac{2 (m^{3} \cdot - 12 n^{3})}{2}$

Step 10.2

Cancel the common factors.

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Step 10.2.1

Factor $2$ out of $2$ .

$\frac{2 (m^{3} \cdot - 12 n^{3})}{2 (1)}$

Step 10.2.2

Cancel the common factor.

$\frac{2 (m^{3} \cdot - 12 n^{3})}{2 \cdot 1}$

Step 10.2.3

Rewrite the expression.

$\frac{m^{3} \cdot - 12 n^{3}}{1}$

Step 10.2.4

Divide $m^{3} \cdot - 12 n^{3}$ by $1$ .

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

Step 11

Move $- 12$ to the left of $m^{3}$ .

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