Algebra Examples

$\frac{3 a}{4 b^{5}} \cdot \frac{12 b^{2}}{9 a}$

Step 1

Combine.

$\frac{3 a (12 b^{2})}{4 b^{5} (9 a)}$

Step 2

Cancel the common factor of $3$ and $9$ .

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Step 2.1

Factor $3$ out of $3 a (12 b^{2})$ .

$\frac{3 (a (12 b^{2}))}{4 b^{5} (9 a)}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $3$ out of $4 b^{5} (9 a)$ .

$\frac{3 (a (12 b^{2}))}{3 (4 b^{5} (3 a))}$

Step 2.2.2

Cancel the common factor.

$\frac{3 (a (12 b^{2}))}{3 (4 b^{5} (3 a))}$

Step 2.2.3

Rewrite the expression.

$\frac{a (12 b^{2})}{4 b^{5} (3 a)}$

$\frac{a (12 b^{2})}{4 b^{5} (3 a)}$

$\frac{a (12 b^{2})}{4 b^{5} (3 a)}$

Step 3

Cancel the common factor of $a$ .

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Step 3.1

Cancel the common factor.

$\frac{a (12 b^{2})}{4 b^{5} (3 a)}$

Step 3.2

Rewrite the expression.

$\frac{12 b^{2}}{4 b^{5} \cdot (3)}$

$\frac{12 b^{2}}{4 b^{5} \cdot (3)}$

Step 4

Cancel the common factor of $12$ and $4$ .

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Step 4.1

Factor $4$ out of $12 b^{2}$ .

$\frac{4 (3 b^{2})}{4 b^{5} \cdot (3)}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $4$ out of $4 b^{5} \cdot (3)$ .

$\frac{4 (3 b^{2})}{4 (b^{5} \cdot (3))}$

Step 4.2.2

Cancel the common factor.

$\frac{4 (3 b^{2})}{4 (b^{5} \cdot (3))}$

Step 4.2.3

Rewrite the expression.

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

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

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

Step 5

Cancel the common factor of $3$ .

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Step 5.1

Cancel the common factor.

$\frac{3 b^{2}}{b^{5} \cdot 3}$

Step 5.2

Rewrite the expression.

$\frac{b^{2}}{b^{5}}$

$\frac{b^{2}}{b^{5}}$

Step 6

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

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Step 6.1

Multiply by $1$ .

$\frac{b^{2} \cdot 1}{b^{5}}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

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

$\frac{b^{2} \cdot 1}{b^{2} b^{3}}$

Step 6.2.2

Cancel the common factor.

$\frac{b^{2} \cdot 1}{b^{2} b^{3}}$

Step 6.2.3

Rewrite the expression.

$\frac{1}{b^{3}}$

$\frac{1}{b^{3}}$

$\frac{1}{b^{3}}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$