Pre-Algebra Examples

$\frac{1 w^{13} z^{6}}{2 w^{5}} \div \frac{12 w^{4} z^{8}}{1 z^{3}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{1 w^{13} z^{6}}{2 w^{5}} \cdot \frac{1 z^{3}}{12 w^{4} z^{8}}$

Step 2

Combine.

$\frac{1 w^{13} z^{6} (1 z^{3})}{2 w^{5} (12 w^{4} z^{8})}$

Step 3

Multiply $z^{6}$ by $z^{3}$ by adding the exponents.

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Step 3.1

Move $z^{3}$ .

$\frac{1 w^{13} (z^{3} z^{6}) \cdot 1}{2 w^{5} (12 w^{4} z^{8})}$

Step 3.2

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

$\frac{1 w^{13} z^{3 + 6} \cdot 1}{2 w^{5} (12 w^{4} z^{8})}$

Step 3.3

Add $3$ and $6$ .

$\frac{1 w^{13} z^{9} \cdot 1}{2 w^{5} (12 w^{4} z^{8})}$

Step 4

Simplify $1 w^{13} z^{9} \cdot 1$ .

$\frac{w^{13} z^{9}}{2 w^{5} (12 w^{4} z^{8})}$

Step 5

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

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Step 5.1

Move $w^{4}$ .

$\frac{w^{13} z^{9}}{2 (w^{4} w^{5}) (12 z^{8})}$

Step 5.2

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

$\frac{w^{13} z^{9}}{2 w^{4 + 5} (12 z^{8})}$

Step 5.3

Add $4$ and $5$ .

$\frac{w^{13} z^{9}}{2 w^{9} (12 z^{8})}$

Step 6

Cancel the common factor of $w^{13}$ and $w^{9}$ .

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Step 6.1

Factor $w^{9}$ out of $w^{13} z^{9}$ .

$\frac{w^{9} (w^{4} z^{9})}{2 w^{9} (12 z^{8})}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $w^{9}$ out of $2 w^{9} (12 z^{8})$ .

$\frac{w^{9} (w^{4} z^{9})}{w^{9} (2 (12 z^{8}))}$

Step 6.2.2

Cancel the common factor.

$\frac{w^{9} (w^{4} z^{9})}{w^{9} (2 (12 z^{8}))}$

Step 6.2.3

Rewrite the expression.

$\frac{w^{4} z^{9}}{2 (12 z^{8})}$

Step 7

Cancel the common factor of $z^{9}$ and $z^{8}$ .

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Step 7.1

Factor $z^{8}$ out of $w^{4} z^{9}$ .

$\frac{z^{8} (w^{4} z)}{2 (12 z^{8})}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $z^{8}$ out of $2 (12 z^{8})$ .

$\frac{z^{8} (w^{4} z)}{z^{8} (2 \cdot (12))}$

Step 7.2.2

Cancel the common factor.

$\frac{z^{8} (w^{4} z)}{z^{8} (2 \cdot (12))}$

Step 7.2.3

Rewrite the expression.

$\frac{w^{4} z}{2 \cdot (12)}$

Step 8

Multiply $2$ by $12$ .

$\frac{w^{4} z}{24}$