Basic Math Examples

$\frac{3 z^{3}}{2 w^{3}} \div \frac{z w}{2 w^{2}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{3 z^{3}}{2 w^{3}} \cdot \frac{2 w^{2}}{z w}$

Step 2

Combine.

$\frac{3 z^{3} (2 w^{2})}{2 w^{3} (z w)}$

Step 3

Multiply $w^{3}$ by $w$ by adding the exponents.

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Step 3.1

Move $w$ .

$\frac{3 z^{3} (2 w^{2})}{2 (w \cdot w^{3}) z}$

Step 3.2

Multiply $w$ by $w^{3}$ .

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Step 3.2.1

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

$\frac{3 z^{3} (2 w^{2})}{2 (w^{1} w^{3}) z}$

Step 3.2.2

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

$\frac{3 z^{3} (2 w^{2})}{2 w^{1 + 3} z}$

Step 3.3

Add $1$ and $3$ .

$\frac{3 z^{3} (2 w^{2})}{2 w^{4} z}$

Step 4

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

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Step 4.1

Factor $z$ out of $3 z^{3} (2 w^{2})$ .

$\frac{z (3 z^{2} (2 w^{2}))}{2 w^{4} z}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $z$ out of $2 w^{4} z$ .

$\frac{z (3 z^{2} (2 w^{2}))}{z (2 w^{4})}$

Step 4.2.2

Cancel the common factor.

$\frac{z (3 z^{2} (2 w^{2}))}{z (2 w^{4})}$

Step 4.2.3

Rewrite the expression.

$\frac{3 z^{2} (2 w^{2})}{2 w^{4}}$

Step 5

Cancel the common factor of $2$ .

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Step 5.1

Cancel the common factor.

$\frac{3 z^{2} (2 w^{2})}{2 w^{4}}$

Step 5.2

Rewrite the expression.

$\frac{3 z^{2} (w^{2})}{w^{4}}$

Step 6

Cancel the common factor of $w^{2}$ and $w^{4}$ .

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Step 6.1

Factor $w^{2}$ out of $3 z^{2} (w^{2})$ .

$\frac{w^{2} (3 z^{2})}{w^{4}}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $w^{2}$ out of $w^{4}$ .

$\frac{w^{2} (3 z^{2})}{w^{2} w^{2}}$

Step 6.2.2

Cancel the common factor.

$\frac{w^{2} (3 z^{2})}{w^{2} w^{2}}$

Step 6.2.3

Rewrite the expression.

$\frac{3 z^{2}}{w^{2}}$