Algebra Examples

$\frac{24 x^{3}}{25 y^{5}} \cdot \frac{15 y^{2}}{8 x^{2}}$

Step 1

Combine.

$\frac{24 x^{3} (15 y^{2})}{25 y^{5} (8 x^{2})}$

Step 2

Cancel the common factor of $24$ and $8$ .

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Step 2.1

Factor $8$ out of $24 x^{3} (15 y^{2})$ .

$\frac{8 (3 x^{3} (15 y^{2}))}{25 y^{5} (8 x^{2})}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $8$ out of $25 y^{5} (8 x^{2})$ .

$\frac{8 (3 x^{3} (15 y^{2}))}{8 (25 y^{5} (x^{2}))}$

Step 2.2.2

Cancel the common factor.

$\frac{8 (3 x^{3} (15 y^{2}))}{8 (25 y^{5} (x^{2}))}$

Step 2.2.3

Rewrite the expression.

$\frac{3 x^{3} (15 y^{2})}{25 y^{5} (x^{2})}$

Step 3

Cancel the common factor of $x^{3}$ and $x^{2}$ .

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Step 3.1

Factor $x^{2}$ out of $3 x^{3} (15 y^{2})$ .

$\frac{x^{2} (3 x (15 y^{2}))}{25 y^{5} (x^{2})}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $x^{2}$ out of $25 y^{5} (x^{2})$ .

$\frac{x^{2} (3 x (15 y^{2}))}{x^{2} (25 y^{5})}$

Step 3.2.2

Cancel the common factor.

$\frac{x^{2} (3 x (15 y^{2}))}{x^{2} (25 y^{5})}$

Step 3.2.3

Rewrite the expression.

$\frac{3 x (15 y^{2})}{25 y^{5}}$

Step 4

Cancel the common factor of $15$ and $25$ .

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Step 4.1

Factor $5$ out of $3 x (15 y^{2})$ .

$\frac{5 (3 x (3 y^{2}))}{25 y^{5}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $5$ out of $25 y^{5}$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 5

Cancel the common factor of $y^{2}$ and $y^{5}$ .

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Step 5.1

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

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

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $y^{2}$ out of $5 y^{5}$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

Step 6

Multiply $3$ by $3$ .

$\frac{9 x}{5 y^{3}}$