Pre-Algebra Examples

$\frac{2 x^{4}}{15 a^{5}} \div \frac{x}{9 a^{3}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{2 x^{4}}{15 a^{5}} \cdot \frac{9 a^{3}}{x}$

Step 2

Combine.

$\frac{2 x^{4} (9 a^{3})}{15 a^{5} x}$

Step 3

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

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Step 3.1

Factor $x$ out of $2 x^{4} (9 a^{3})$ .

$\frac{x (2 x^{3} (9 a^{3}))}{15 a^{5} x}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $x$ out of $15 a^{5} x$ .

$\frac{x (2 x^{3} (9 a^{3}))}{x (15 a^{5})}$

Step 3.2.2

Cancel the common factor.

$\frac{x (2 x^{3} (9 a^{3}))}{x (15 a^{5})}$

Step 3.2.3

Rewrite the expression.

$\frac{2 x^{3} (9 a^{3})}{15 a^{5}}$

Step 4

Cancel the common factor of $9$ and $15$ .

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Step 4.1

Factor $3$ out of $2 x^{3} (9 a^{3})$ .

$\frac{3 (2 x^{3} (3 a^{3}))}{15 a^{5}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $3$ out of $15 a^{5}$ .

$\frac{3 (2 x^{3} (3 a^{3}))}{3 (5 a^{5})}$

Step 4.2.2

Cancel the common factor.

$\frac{3 (2 x^{3} (3 a^{3}))}{3 (5 a^{5})}$

Step 4.2.3

Rewrite the expression.

$\frac{2 x^{3} (3 a^{3})}{5 a^{5}}$

Step 5

Cancel the common factor of $a^{3}$ and $a^{5}$ .

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Step 5.1

Factor $a^{3}$ out of $2 x^{3} (3 a^{3})$ .

$\frac{a^{3} (2 x^{3} \cdot (3))}{5 a^{5}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $a^{3}$ out of $5 a^{5}$ .

$\frac{a^{3} (2 x^{3} \cdot (3))}{a^{3} (5 a^{2})}$

Step 5.2.2

Cancel the common factor.

$\frac{a^{3} (2 x^{3} \cdot (3))}{a^{3} (5 a^{2})}$

Step 5.2.3

Rewrite the expression.

$\frac{2 x^{3} \cdot (3)}{5 a^{2}}$

Step 6

Multiply $3$ by $2$ .

$\frac{6 x^{3}}{5 a^{2}}$