Algebra Examples

$\frac{4 p^{3} q}{6 p^{2} q^{2}} \div \frac{12 p q^{3}}{2 p^{2} q^{2}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{4 p^{3} q}{6 p^{2} q^{2}} \cdot \frac{2 p^{2} q^{2}}{12 p q^{3}}$

Step 2

Combine.

$\frac{4 p^{3} q (2 p^{2} q^{2})}{6 p^{2} q^{2} (12 p q^{3})}$

Step 3

Multiply $p^{3}$ by $p^{2}$ by adding the exponents.

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Step 3.1

Move $p^{2}$ .

$\frac{4 (p^{2} p^{3}) q (2 q^{2})}{6 p^{2} q^{2} (12 p q^{3})}$

Step 3.2

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

$\frac{4 p^{2 + 3} q (2 q^{2})}{6 p^{2} q^{2} (12 p q^{3})}$

Step 3.3

Add $2$ and $3$ .

$\frac{4 p^{5} q (2 q^{2})}{6 p^{2} q^{2} (12 p q^{3})}$

Step 4

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

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Step 4.1

Move $q^{2}$ .

$\frac{4 p^{5} (q^{2} q) \cdot 2}{6 p^{2} q^{2} (12 p q^{3})}$

Step 4.2

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

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Step 4.2.1

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

$\frac{4 p^{5} (q^{2} q^{1}) \cdot 2}{6 p^{2} q^{2} (12 p q^{3})}$

Step 4.2.2

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

$\frac{4 p^{5} q^{2 + 1} \cdot 2}{6 p^{2} q^{2} (12 p q^{3})}$

Step 4.3

Add $2$ and $1$ .

$\frac{4 p^{5} q^{3} \cdot 2}{6 p^{2} q^{2} (12 p q^{3})}$

Step 5

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

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Step 5.1

Move $p$ .

$\frac{4 p^{5} q^{3} \cdot 2}{6 (p \cdot p^{2}) q^{2} (12 q^{3})}$

Step 5.2

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

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Step 5.2.1

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

$\frac{4 p^{5} q^{3} \cdot 2}{6 (p^{1} p^{2}) q^{2} (12 q^{3})}$

Step 5.2.2

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

$\frac{4 p^{5} q^{3} \cdot 2}{6 p^{1 + 2} q^{2} (12 q^{3})}$

Step 5.3

Add $1$ and $2$ .

$\frac{4 p^{5} q^{3} \cdot 2}{6 p^{3} q^{2} (12 q^{3})}$

Step 6

Multiply $q^{2}$ by $q^{3}$ by adding the exponents.

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Step 6.1

Move $q^{3}$ .

$\frac{4 p^{5} q^{3} \cdot 2}{6 p^{3} (q^{3} q^{2}) \cdot 12}$

Step 6.2

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

$\frac{4 p^{5} q^{3} \cdot 2}{6 p^{3} q^{3 + 2} \cdot 12}$

Step 6.3

Add $3$ and $2$ .

$\frac{4 p^{5} q^{3} \cdot 2}{6 p^{3} q^{5} \cdot 12}$

Step 7

Cancel the common factor of $4$ and $6$ .

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Step 7.1

Factor $2$ out of $4 p^{5} q^{3} \cdot 2$ .

$\frac{2 (2 p^{5} q^{3} \cdot 2)}{6 p^{3} q^{5} \cdot 12}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $2$ out of $6 p^{3} q^{5} \cdot 12$ .

$\frac{2 (2 p^{5} q^{3} \cdot 2)}{2 (3 p^{3} q^{5} \cdot 12)}$

Step 7.2.2

Cancel the common factor.

$\frac{2 (2 p^{5} q^{3} \cdot 2)}{2 (3 p^{3} q^{5} \cdot 12)}$

Step 7.2.3

Rewrite the expression.

$\frac{2 p^{5} q^{3} \cdot 2}{3 p^{3} q^{5} \cdot 12}$

Step 8

Cancel the common factor of $2$ and $12$ .

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Step 8.1

Factor $2$ out of $2 p^{5} q^{3} \cdot 2$ .

$\frac{2 (p^{5} q^{3} \cdot 2)}{3 p^{3} q^{5} \cdot 12}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $2$ out of $3 p^{3} q^{5} \cdot 12$ .

$\frac{2 (p^{5} q^{3} \cdot 2)}{2 (3 p^{3} q^{5} \cdot 6)}$

Step 8.2.2

Cancel the common factor.

$\frac{2 (p^{5} q^{3} \cdot 2)}{2 (3 p^{3} q^{5} \cdot 6)}$

Step 8.2.3

Rewrite the expression.

$\frac{p^{5} q^{3} \cdot 2}{3 p^{3} q^{5} \cdot 6}$

Step 9

Cancel the common factor of $p^{5}$ and $p^{3}$ .

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Step 9.1

Factor $p^{3}$ out of $p^{5} q^{3} \cdot 2$ .

$\frac{p^{3} (p^{2} q^{3} \cdot 2)}{3 p^{3} q^{5} \cdot 6}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $p^{3}$ out of $3 p^{3} q^{5} \cdot 6$ .

$\frac{p^{3} (p^{2} q^{3} \cdot 2)}{p^{3} (3 q^{5} \cdot 6)}$

Step 9.2.2

Cancel the common factor.

$\frac{p^{3} (p^{2} q^{3} \cdot 2)}{p^{3} (3 q^{5} \cdot 6)}$

Step 9.2.3

Rewrite the expression.

$\frac{p^{2} q^{3} \cdot 2}{3 q^{5} \cdot 6}$

Step 10

Cancel the common factor of $q^{3}$ and $q^{5}$ .

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Step 10.1

Factor $q^{3}$ out of $p^{2} q^{3} \cdot 2$ .

$\frac{q^{3} (p^{2} \cdot 2)}{3 q^{5} \cdot 6}$

Step 10.2

Cancel the common factors.

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Step 10.2.1

Factor $q^{3}$ out of $3 q^{5} \cdot 6$ .

$\frac{q^{3} (p^{2} \cdot 2)}{q^{3} (3 q^{2} \cdot 6)}$

Step 10.2.2

Cancel the common factor.

$\frac{q^{3} (p^{2} \cdot 2)}{q^{3} (3 q^{2} \cdot 6)}$

Step 10.2.3

Rewrite the expression.

$\frac{p^{2} \cdot 2}{3 q^{2} \cdot 6}$

Step 11

Cancel the common factor of $2$ and $6$ .

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Step 11.1

Factor $2$ out of $p^{2} \cdot 2$ .

$\frac{2 \cdot p^{2}}{3 q^{2} \cdot 6}$

Step 11.2

Cancel the common factors.

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Step 11.2.1

Factor $2$ out of $3 q^{2} \cdot 6$ .

$\frac{2 \cdot p^{2}}{2 (3 q^{2} \cdot 3)}$

Step 11.2.2

Cancel the common factor.

$\frac{2 \cdot p^{2}}{2 (3 q^{2} \cdot 3)}$

Step 11.2.3

Rewrite the expression.

$\frac{p^{2}}{3 q^{2} \cdot 3}$

Step 12

Multiply $3$ by $3$ .

$\frac{p^{2}}{9 q^{2}}$