Pre-Algebra Examples

$\frac{18 x^{4}}{2 x^{8}} \div \frac{81 x}{6 x^{8}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{18 x^{4}}{2 x^{8}} \cdot \frac{6 x^{8}}{81 x}$

Step 2

Combine.

$\frac{18 x^{4} (6 x^{8})}{2 x^{8} (81 x)}$

Step 3

Multiply $x^{4}$ by $x^{8}$ by adding the exponents.

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Step 3.1

Move $x^{8}$ .

$\frac{18 (x^{8} x^{4}) \cdot 6}{2 x^{8} (81 x)}$

Step 3.2

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

$\frac{18 x^{8 + 4} \cdot 6}{2 x^{8} (81 x)}$

Step 3.3

Add $8$ and $4$ .

$\frac{18 x^{12} \cdot 6}{2 x^{8} (81 x)}$

Step 4

Multiply $x^{8}$ by $x$ by adding the exponents.

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Step 4.1

Move $x$ .

$\frac{18 x^{12} \cdot 6}{2 (x \cdot x^{8}) \cdot 81}$

Step 4.2

Multiply $x$ by $x^{8}$ .

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Step 4.2.1

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

$\frac{18 x^{12} \cdot 6}{2 (x^{1} x^{8}) \cdot 81}$

Step 4.2.2

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

$\frac{18 x^{12} \cdot 6}{2 x^{1 + 8} \cdot 81}$

Step 4.3

Add $1$ and $8$ .

$\frac{18 x^{12} \cdot 6}{2 x^{9} \cdot 81}$

Step 5

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

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Step 5.1

Factor $2$ out of $18 x^{12} \cdot 6$ .

$\frac{2 (9 x^{12} \cdot 6)}{2 x^{9} \cdot 81}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $2$ out of $2 x^{9} \cdot 81$ .

$\frac{2 (9 x^{12} \cdot 6)}{2 (x^{9} \cdot 81)}$

Step 5.2.2

Cancel the common factor.

$\frac{2 (9 x^{12} \cdot 6)}{2 (x^{9} \cdot 81)}$

Step 5.2.3

Rewrite the expression.

$\frac{9 x^{12} \cdot 6}{x^{9} \cdot 81}$

Step 6

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

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Step 6.1

Factor $9$ out of $9 x^{12} \cdot 6$ .

$\frac{9 (x^{12} \cdot 6)}{x^{9} \cdot 81}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

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

$\frac{9 (x^{12} \cdot 6)}{9 (x^{9} \cdot 9)}$

Step 6.2.2

Cancel the common factor.

$\frac{9 (x^{12} \cdot 6)}{9 (x^{9} \cdot 9)}$

Step 6.2.3

Rewrite the expression.

$\frac{x^{12} \cdot 6}{x^{9} \cdot 9}$

Step 7

Cancel the common factor of $x^{12}$ and $x^{9}$ .

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Step 7.1

Factor $x^{9}$ out of $x^{12} \cdot 6$ .

$\frac{x^{9} (x^{3} \cdot 6)}{x^{9} \cdot 9}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $x^{9}$ out of $x^{9} \cdot 9$ .

$\frac{x^{9} (x^{3} \cdot 6)}{x^{9} (9)}$

Step 7.2.2

Cancel the common factor.

$\frac{x^{9} (x^{3} \cdot 6)}{x^{9} \cdot 9}$

Step 7.2.3

Rewrite the expression.

$\frac{x^{3} \cdot 6}{9}$

Step 8

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

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Step 8.1

Factor $3$ out of $x^{3} \cdot 6$ .

$\frac{3 (x^{3} \cdot 2)}{9}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $3$ out of $9$ .

$\frac{3 (x^{3} \cdot 2)}{3 (3)}$

Step 8.2.2

Cancel the common factor.

$\frac{3 (x^{3} \cdot 2)}{3 \cdot 3}$

Step 8.2.3

Rewrite the expression.

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

Step 9

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

$\frac{2 x^{3}}{3}$