Algebra Examples

$\frac{- 12 n^{7} p^{5} (n^{2} p^{4})}{36 n^{6} p^{7}}$

Step 1

Multiply $n^{7}$ by $n^{2}$ by adding the exponents.

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Step 1.1

Move $n^{2}$ .

$\frac{- 12 (n^{2} n^{7}) p^{5} p^{4}}{36 n^{6} p^{7}}$

Step 1.2

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

$\frac{- 12 n^{2 + 7} p^{5} p^{4}}{36 n^{6} p^{7}}$

Step 1.3

Add $2$ and $7$ .

$\frac{- 12 n^{9} p^{5} p^{4}}{36 n^{6} p^{7}}$

Step 2

Multiply $p^{5}$ by $p^{4}$ by adding the exponents.

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Step 2.1

Move $p^{4}$ .

$\frac{- 12 n^{9} (p^{4} p^{5})}{36 n^{6} p^{7}}$

Step 2.2

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

$\frac{- 12 n^{9} p^{4 + 5}}{36 n^{6} p^{7}}$

Step 2.3

Add $4$ and $5$ .

$\frac{- 12 n^{9} p^{9}}{36 n^{6} p^{7}}$

Step 3

Cancel the common factor of $- 12$ and $36$ .

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Step 3.1

Factor $12$ out of $- 12 n^{9} p^{9}$ .

$\frac{12 (- n^{9} p^{9})}{36 n^{6} p^{7}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $12$ out of $36 n^{6} p^{7}$ .

$\frac{12 (- n^{9} p^{9})}{12 (3 n^{6} p^{7})}$

Step 3.2.2

Cancel the common factor.

$\frac{12 (- n^{9} p^{9})}{12 (3 n^{6} p^{7})}$

Step 3.2.3

Rewrite the expression.

$\frac{- n^{9} p^{9}}{3 n^{6} p^{7}}$

Step 4

Cancel the common factor of $n^{9}$ and $n^{6}$ .

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Step 4.1

Factor $n^{6}$ out of $- n^{9} p^{9}$ .

$\frac{n^{6} (- n^{3} p^{9})}{3 n^{6} p^{7}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $n^{6}$ out of $3 n^{6} p^{7}$ .

$\frac{n^{6} (- n^{3} p^{9})}{n^{6} (3 p^{7})}$

Step 4.2.2

Cancel the common factor.

$\frac{n^{6} (- n^{3} p^{9})}{n^{6} (3 p^{7})}$

Step 4.2.3

Rewrite the expression.

$\frac{- n^{3} p^{9}}{3 p^{7}}$

Step 5

Cancel the common factor of $p^{9}$ and $p^{7}$ .

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Step 5.1

Factor $p^{7}$ out of $- n^{3} p^{9}$ .

$\frac{p^{7} (- n^{3} p^{2})}{3 p^{7}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $p^{7}$ out of $3 p^{7}$ .

$\frac{p^{7} (- n^{3} p^{2})}{p^{7} \cdot 3}$

Step 5.2.2

Cancel the common factor.

$\frac{p^{7} (- n^{3} p^{2})}{p^{7} \cdot 3}$

Step 5.2.3

Rewrite the expression.

$\frac{- n^{3} p^{2}}{3}$

Step 6

Move the negative in front of the fraction.

$- \frac{n^{3} p^{2}}{3}$