Basic Math Examples

\frac{18 a^{9}}{2 y^{10}} \div \frac{81 a^{7}}{6 y^{7}}

$\frac{18 a^{9}}{2 y^{10}} \div \frac{81 a^{7}}{6 y^{7}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

\frac{18 a^{9}}{2 y^{10}} \cdot \frac{6 y^{7}}{81 a^{7}}

$\frac{18 a^{9}}{2 y^{10}} \cdot \frac{6 y^{7}}{81 a^{7}}$

Step 2

Combine.

\frac{18 a^{9} (6 y^{7})}{2 y^{10} (81 a^{7})}

$\frac{18 a^{9} (6 y^{7})}{2 y^{10} (81 a^{7})}$

Step 3

Cancel the common factor of

18

$18$ and

2

$2$ .

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Step 3.1

Factor

2

$2$ out of

18 a^{9} (6 y^{7})

$18 a^{9} (6 y^{7})$ .

\frac{2 (9 a^{9} (6 y^{7}))}{2 y^{10} (81 a^{7})}

$\frac{2 (9 a^{9} (6 y^{7}))}{2 y^{10} (81 a^{7})}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor

2

$2$ out of

2 y^{10} (81 a^{7})

$2 y^{10} (81 a^{7})$ .

\frac{2 (9 a^{9} (6 y^{7}))}{2 (y^{10} (81 a^{7}))}

$\frac{2 (9 a^{9} (6 y^{7}))}{2 (y^{10} (81 a^{7}))}$

Step 3.2.2

Cancel the common factor.

$\frac{2 (9 a^{9} (6 y^{7}))}{2 (y^{10} (81 a^{7}))}$

Step 3.2.3

Rewrite the expression.

$\frac{9 a^{9} (6 y^{7})}{y^{10} (81 a^{7})}$

Step 4

Cancel the common factor of

$9$ and

$81$ .

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Step 4.1

Factor

$9$ out of

$9 a^{9} (6 y^{7})$ .

$\frac{9 (a^{9} (6 y^{7}))}{y^{10} (81 a^{7})}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor

$9$ out of

$y^{10} (81 a^{7})$ .

$\frac{9 (a^{9} (6 y^{7}))}{9 (y^{10} (9 a^{7}))}$

Step 4.2.2

Cancel the common factor.

$\frac{9 (a^{9} (6 y^{7}))}{9 (y^{10} (9 a^{7}))}$

Step 4.2.3

Rewrite the expression.

$\frac{a^{9} (6 y^{7})}{y^{10} (9 a^{7})}$

Step 5

Cancel the common factor of

$a^{9}$ and

$a^{7}$ .

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Step 5.1

Factor

$a^{7}$ out of

$a^{9} (6 y^{7})$ .

$\frac{a^{7} (a^{2} (6 y^{7}))}{y^{10} (9 a^{7})}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor

$a^{7}$ out of

$y^{10} (9 a^{7})$ .

$\frac{a^{7} (a^{2} (6 y^{7}))}{a^{7} (y^{10} \cdot (9))}$

Step 5.2.2

Cancel the common factor.

$\frac{a^{7} (a^{2} (6 y^{7}))}{a^{7} (y^{10} \cdot (9))}$

Step 5.2.3

Rewrite the expression.

$\frac{a^{2} (6 y^{7})}{y^{10} \cdot (9)}$

Step 6

Cancel the common factor of

$6$ and

$9$ .

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Step 6.1

Factor

$3$ out of

$a^{2} (6 y^{7})$ .

$\frac{3 (a^{2} (2 y^{7}))}{y^{10} \cdot (9)}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor

$3$ out of

$y^{10} \cdot (9)$ .

$\frac{3 (a^{2} (2 y^{7}))}{3 (y^{10} \cdot (3))}$

Step 6.2.2

Cancel the common factor.

$\frac{3 (a^{2} (2 y^{7}))}{3 (y^{10} \cdot (3))}$

Step 6.2.3

Rewrite the expression.

$\frac{a^{2} (2 y^{7})}{y^{10} \cdot (3)}$

Step 7

Cancel the common factor of

$y^{7}$ and

$y^{10}$ .

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Step 7.1

Factor

$y^{7}$ out of

$a^{2} (2 y^{7})$ .

$\frac{y^{7} (a^{2} \cdot (2))}{y^{10} \cdot (3)}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor

$y^{7}$ out of

$y^{10} \cdot (3)$ .

$\frac{y^{7} (a^{2} \cdot (2))}{y^{7} (y^{3} \cdot 3)}$

Step 7.2.2

Cancel the common factor.

$\frac{y^{7} (a^{2} \cdot (2))}{y^{7} (y^{3} \cdot 3)}$

Step 7.2.3

Rewrite the expression.

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

Step 8

Reorder.

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Step 8.1

Move

$2$ to the left of

$a^{2}$ .

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

Step 8.2

Move

$3$ to the left of

$y^{3}$ .

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