Pre-Algebra Examples

$\frac{35 x^{8}}{7 x^{9}} \div \frac{5 x^{5}}{9 x^{6}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{35 x^{8}}{7 x^{9}} \cdot \frac{9 x^{6}}{5 x^{5}}$

Step 2

Combine.

$\frac{35 x^{8} (9 x^{6})}{7 x^{9} (5 x^{5})}$

Step 3

Multiply $x^{8}$ by $x^{6}$ by adding the exponents.

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Step 3.1

Move $x^{6}$ .

$\frac{35 (x^{6} x^{8}) \cdot 9}{7 x^{9} (5 x^{5})}$

Step 3.2

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

$\frac{35 x^{6 + 8} \cdot 9}{7 x^{9} (5 x^{5})}$

Step 3.3

Add $6$ and $8$ .

$\frac{35 x^{14} \cdot 9}{7 x^{9} (5 x^{5})}$

Step 4

Multiply $x^{9}$ by $x^{5}$ by adding the exponents.

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Step 4.1

Move $x^{5}$ .

$\frac{35 x^{14} \cdot 9}{7 (x^{5} x^{9}) \cdot 5}$

Step 4.2

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

$\frac{35 x^{14} \cdot 9}{7 x^{5 + 9} \cdot 5}$

Step 4.3

Add $5$ and $9$ .

$\frac{35 x^{14} \cdot 9}{7 x^{14} \cdot 5}$

Step 5

Cancel the common factor of $35$ and $7$ .

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Step 5.1

Factor $7$ out of $35 x^{14} \cdot 9$ .

$\frac{7 (5 x^{14} \cdot 9)}{7 x^{14} \cdot 5}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $7$ out of $7 x^{14} \cdot 5$ .

$\frac{7 (5 x^{14} \cdot 9)}{7 (x^{14} \cdot 5)}$

Step 5.2.2

Cancel the common factor.

$\frac{7 (5 x^{14} \cdot 9)}{7 (x^{14} \cdot 5)}$

Step 5.2.3

Rewrite the expression.

$\frac{5 x^{14} \cdot 9}{x^{14} \cdot 5}$

Step 6

Cancel the common factor of $5$ .

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Step 6.1

Cancel the common factor.

$\frac{5 x^{14} \cdot 9}{x^{14} \cdot 5}$

Step 6.2

Rewrite the expression.

$\frac{x^{14} \cdot 9}{x^{14}}$

Step 7

Cancel the common factor of $x^{14}$ .

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Step 7.1

Cancel the common factor.

$\frac{x^{14} \cdot 9}{x^{14}}$

Step 7.2

Divide $9$ by $1$ .

$9$