Finite Math Examples

$(12 m^{2} n^{2}) (- 8 m n) + 1$

Step 1

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

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Step 1.1

Move $m$ .

$12 (m \cdot m^{2}) n^{2} (- 8 n) + 1$

Step 1.2

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

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Step 1.2.1

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

$12 (m^{1} m^{2}) n^{2} (- 8 n) + 1$

Step 1.2.2

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

$12 m^{1 + 2} n^{2} (- 8 n) + 1$

Step 1.3

Add $1$ and $2$ .

$12 m^{3} n^{2} (- 8 n) + 1$

Step 2

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

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Step 2.1

Move $n$ .

$12 m^{3} (n \cdot n^{2}) \cdot - 8 + 1$

Step 2.2

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

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Step 2.2.1

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

$12 m^{3} (n^{1} n^{2}) \cdot - 8 + 1$

Step 2.2.2

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

$12 m^{3} n^{1 + 2} \cdot - 8 + 1$

Step 2.3

Add $1$ and $2$ .

$12 m^{3} n^{3} \cdot - 8 + 1$

Step 3

Multiply $- 8$ by $12$ .

$- 96 m^{3} n^{3} + 1$

Step 4

Factor $- 1$ out of $- 96 m^{3} n^{3} + 1$ .

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Step 4.1

Factor $- 1$ out of $- 96 m^{3} n^{3}$ .

$- (96 m^{3} n^{3}) + 1$

Step 4.2

Rewrite $1$ as $- 1 (- 1)$ .

$- (96 m^{3} n^{3}) - 1 (- 1)$

Step 4.3

Factor $- 1$ out of $- (96 m^{3} n^{3}) - 1 (- 1)$ .

$- (96 m^{3} n^{3} - 1)$