Algebra Examples

$\frac{6 a^{2}}{5 b^{2}} \cdot \frac{45 b^{3}}{18 a^{3}}$

Step 1

Combine.

$\frac{6 a^{2} (45 b^{3})}{5 b^{2} (18 a^{3})}$

Step 2

Cancel the common factor of $6$ and $18$ .

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Step 2.1

Factor $6$ out of $6 a^{2} (45 b^{3})$ .

$\frac{6 (a^{2} (45 b^{3}))}{5 b^{2} (18 a^{3})}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $6$ out of $5 b^{2} (18 a^{3})$ .

$\frac{6 (a^{2} (45 b^{3}))}{6 (5 b^{2} (3 a^{3}))}$

Step 2.2.2

Cancel the common factor.

$\frac{6 (a^{2} (45 b^{3}))}{6 (5 b^{2} (3 a^{3}))}$

Step 2.2.3

Rewrite the expression.

$\frac{a^{2} (45 b^{3})}{5 b^{2} (3 a^{3})}$

$\frac{a^{2} (45 b^{3})}{5 b^{2} (3 a^{3})}$

$\frac{a^{2} (45 b^{3})}{5 b^{2} (3 a^{3})}$

Step 3

Cancel the common factors.

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Step 3.1

Factor $a^{2}$ out of $5 b^{2} (3 a^{3})$ .

$\frac{a^{2} (45 b^{3})}{a^{2} (5 b^{2} (3 a))}$

Step 3.2

Cancel the common factor.

$\frac{a^{2} (45 b^{3})}{a^{2} (5 b^{2} (3 a))}$

Step 3.3

Rewrite the expression.

$\frac{45 b^{3}}{5 b^{2} (3 a)}$

$\frac{45 b^{3}}{5 b^{2} (3 a)}$

Step 4

Cancel the common factor of $45$ and $5$ .

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Step 4.1

Factor $5$ out of $45 b^{3}$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $5$ out of $5 b^{2} (3 a)$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

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

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

Step 5

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

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Step 5.1

Factor $3$ out of $9 b^{3}$ .

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

Step 5.2

Cancel the common factors.

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Step 5.2.1

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

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

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

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

Step 6

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

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Step 6.1

Factor $b^{2}$ out of $3 b^{3}$ .

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

Step 6.2

Cancel the common factors.

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Step 6.2.1

Cancel the common factor.

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

Step 6.2.2

Rewrite the expression.

$\frac{3 b}{a}$

$\frac{3 b}{a}$

$\frac{3 b}{a}$

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