Pre-Algebra Examples

$\frac{8 x^{3}}{27 y^{8}} \cdot \frac{9 y^{3}}{12 x^{2}}$

Step 1

Simplify and reorder the polynomial.

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Step 1.1

Combine.

$\frac{8 x^{3} (9 y^{3})}{27 y^{8} (12 x^{2})}$

Step 1.2

Cancel the common factor of $8$ and $12$ .

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Step 1.2.1

Factor $4$ out of $8 x^{3} (9 y^{3})$ .

$\frac{4 (2 x^{3} (9 y^{3}))}{27 y^{8} (12 x^{2})}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $4$ out of $27 y^{8} (12 x^{2})$ .

$\frac{4 (2 x^{3} (9 y^{3}))}{4 (27 y^{8} (3 x^{2}))}$

Step 1.2.2.2

Cancel the common factor.

$\frac{4 (2 x^{3} (9 y^{3}))}{4 (27 y^{8} (3 x^{2}))}$

Step 1.2.2.3

Rewrite the expression.

$\frac{2 x^{3} (9 y^{3})}{27 y^{8} (3 x^{2})}$

Step 1.3

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

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Step 1.3.1

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

$\frac{x^{2} (2 x (9 y^{3}))}{27 y^{8} (3 x^{2})}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $x^{2}$ out of $27 y^{8} (3 x^{2})$ .

$\frac{x^{2} (2 x (9 y^{3}))}{x^{2} (27 y^{8} \cdot (3))}$

Step 1.3.2.2

Cancel the common factor.

$\frac{x^{2} (2 x (9 y^{3}))}{x^{2} (27 y^{8} \cdot (3))}$

Step 1.3.2.3

Rewrite the expression.

$\frac{2 x (9 y^{3})}{27 y^{8} \cdot (3)}$

Step 1.4

Cancel the common factor of $9$ and $27$ .

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Step 1.4.1

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

$\frac{9 (2 x (y^{3}))}{27 y^{8} \cdot (3)}$

Step 1.4.2

Cancel the common factors.

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Step 1.4.2.1

Factor $9$ out of $27 y^{8} \cdot (3)$ .

$\frac{9 (2 x (y^{3}))}{9 (3 y^{8} \cdot 3)}$

Step 1.4.2.2

Cancel the common factor.

$\frac{9 (2 x (y^{3}))}{9 (3 y^{8} \cdot 3)}$

Step 1.4.2.3

Rewrite the expression.

$\frac{2 x (y^{3})}{3 y^{8} \cdot 3}$

Step 1.5

Cancel the common factor of $y^{3}$ and $y^{8}$ .

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Step 1.5.1

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

$\frac{y^{3} (2 x)}{3 y^{8} \cdot 3}$

Step 1.5.2

Cancel the common factors.

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Step 1.5.2.1

Factor $y^{3}$ out of $3 y^{8} \cdot 3$ .

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

Step 1.5.2.2

Cancel the common factor.

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

Step 1.5.2.3

Rewrite the expression.

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

Step 1.6

Multiply $3$ by $3$ .

$\frac{2 x}{9 y^{5}}$

Step 2

The degree cannot be determined because $\frac{2 x}{9 y^{5}}$ is not a polynomial.

Not a polynomial