Basic Math Examples

$\frac{18 y^{6}}{2 z^{6}} \cdot \frac{6 z^{4}}{81 y^{4}}$

Step 1

Combine.

$\frac{18 y^{6} (6 z^{4})}{2 z^{6} (81 y^{4})}$

Step 2

Cancel the common factor of $18$ and $2$ .

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Step 2.1

Factor $2$ out of $18 y^{6} (6 z^{4})$ .

$\frac{2 (9 y^{6} (6 z^{4}))}{2 z^{6} (81 y^{4})}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $2 z^{6} (81 y^{4})$ .

$\frac{2 (9 y^{6} (6 z^{4}))}{2 (z^{6} (81 y^{4}))}$

Step 2.2.2

Cancel the common factor.

$\frac{2 (9 y^{6} (6 z^{4}))}{2 (z^{6} (81 y^{4}))}$

Step 2.2.3

Rewrite the expression.

$\frac{9 y^{6} (6 z^{4})}{z^{6} (81 y^{4})}$

Step 3

Cancel the common factor of $9$ and $81$ .

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Step 3.1

Factor $9$ out of $9 y^{6} (6 z^{4})$ .

$\frac{9 (y^{6} (6 z^{4}))}{z^{6} (81 y^{4})}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $9$ out of $z^{6} (81 y^{4})$ .

$\frac{9 (y^{6} (6 z^{4}))}{9 (z^{6} (9 y^{4}))}$

Step 3.2.2

Cancel the common factor.

$\frac{9 (y^{6} (6 z^{4}))}{9 (z^{6} (9 y^{4}))}$

Step 3.2.3

Rewrite the expression.

$\frac{y^{6} (6 z^{4})}{z^{6} (9 y^{4})}$

Step 4

Cancel the common factor of $y^{6}$ and $y^{4}$ .

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Step 4.1

Factor $y^{4}$ out of $y^{6} (6 z^{4})$ .

$\frac{y^{4} (y^{2} (6 z^{4}))}{z^{6} (9 y^{4})}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $y^{4}$ out of $z^{6} (9 y^{4})$ .

$\frac{y^{4} (y^{2} (6 z^{4}))}{y^{4} (z^{6} \cdot (9))}$

Step 4.2.2

Cancel the common factor.

$\frac{y^{4} (y^{2} (6 z^{4}))}{y^{4} (z^{6} \cdot (9))}$

Step 4.2.3

Rewrite the expression.

$\frac{y^{2} (6 z^{4})}{z^{6} \cdot (9)}$

Step 5

Cancel the common factor of $6$ and $9$ .

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Step 5.1

Factor $3$ out of $y^{2} (6 z^{4})$ .

$\frac{3 (y^{2} (2 z^{4}))}{z^{6} \cdot (9)}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $3$ out of $z^{6} \cdot (9)$ .

$\frac{3 (y^{2} (2 z^{4}))}{3 (z^{6} \cdot (3))}$

Step 5.2.2

Cancel the common factor.

$\frac{3 (y^{2} (2 z^{4}))}{3 (z^{6} \cdot (3))}$

Step 5.2.3

Rewrite the expression.

$\frac{y^{2} (2 z^{4})}{z^{6} \cdot (3)}$

Step 6

Cancel the common factor of $z^{4}$ and $z^{6}$ .

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Step 6.1

Factor $z^{4}$ out of $y^{2} (2 z^{4})$ .

$\frac{z^{4} (y^{2} \cdot (2))}{z^{6} \cdot (3)}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $z^{4}$ out of $z^{6} \cdot (3)$ .

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

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

Step 7

Reorder.

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Step 7.1

Move $2$ to the left of $y^{2}$ .

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

Step 7.2

Move $3$ to the left of $z^{2}$ .

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