Basic Math Examples

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

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

Combine.

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

Step 3

Multiply $y^{6}$ by $y^{4}$ by adding the exponents.

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Step 3.1

Move $y^{4}$ .

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

Step 3.2

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

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

Step 3.3

Add $4$ and $6$ .

$\frac{18 y^{10} \cdot 6}{2 y^{6} (81 y^{4})}$

Step 4

Multiply $y^{6}$ by $y^{4}$ by adding the exponents.

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Step 4.1

Move $y^{4}$ .

$\frac{18 y^{10} \cdot 6}{2 (y^{4} y^{6}) \cdot 81}$

Step 4.2

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

$\frac{18 y^{10} \cdot 6}{2 y^{4 + 6} \cdot 81}$

Step 4.3

Add $4$ and $6$ .

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

Step 5

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

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Step 5.1

Factor $2$ out of $18 y^{10} \cdot 6$ .

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

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $2$ out of $2 y^{10} \cdot 81$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

$\frac{9 y^{10} \cdot 6}{y^{10} \cdot 81}$

Step 6

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

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Step 6.1

Factor $9$ out of $9 y^{10} \cdot 6$ .

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

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $9$ out of $y^{10} \cdot 81$ .

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

$\frac{y^{10} \cdot 6}{y^{10} \cdot 9}$

Step 7

Cancel the common factor of $y^{10}$ .

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Step 7.1

Cancel the common factor.

$\frac{y^{10} \cdot 6}{y^{10} \cdot 9}$

Step 7.2

Rewrite the expression.

$\frac{6}{9}$

Step 8

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

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Step 8.1

Factor $3$ out of $6$ .

$\frac{3 (2)}{9}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $3$ out of $9$ .

$\frac{3 \cdot 2}{3 \cdot 3}$

Step 8.2.2

Cancel the common factor.

$\frac{3 \cdot 2}{3 \cdot 3}$

Step 8.2.3

Rewrite the expression.

$\frac{2}{3}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{3}$

Decimal Form:

$0.\overline{6}$