Algebra Examples

$\frac{18 a}{14 b^{2}} \cdot \frac{21 b}{12 a^{2} b}$

Step 1

Combine.

$\frac{18 a (21 b)}{14 b^{2} (12 a^{2} b)}$

Step 2

Multiply $b^{2}$ by $b$ by adding the exponents.

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Step 2.1

Move $b$ .

$\frac{18 a (21 b)}{14 (b \cdot b^{2}) (12 a^{2})}$

Step 2.2

Multiply $b$ by $b^{2}$ .

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Step 2.2.1

Raise $b$ to the power of $1$ .

$\frac{18 a (21 b)}{14 (b^{1} b^{2}) (12 a^{2})}$

Step 2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{18 a (21 b)}{14 b^{1 + 2} (12 a^{2})}$

$\frac{18 a (21 b)}{14 b^{1 + 2} (12 a^{2})}$

Step 2.3

Add $1$ and $2$ .

$\frac{18 a (21 b)}{14 b^{3} (12 a^{2})}$

$\frac{18 a (21 b)}{14 b^{3} (12 a^{2})}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $18$ and $14$ .

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Step 3.1.1

Factor $2$ out of $18 a (21 b)$ .

$\frac{2 (9 a (21 b))}{14 b^{3} (12 a^{2})}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $2$ out of $14 b^{3} (12 a^{2})$ .

$\frac{2 (9 a (21 b))}{2 (7 b^{3} (12 a^{2}))}$

Step 3.1.2.2

Cancel the common factor.

$\frac{2 (9 a (21 b))}{2 (7 b^{3} (12 a^{2}))}$

Step 3.1.2.3

Rewrite the expression.

$\frac{9 a (21 b)}{7 b^{3} (12 a^{2})}$

$\frac{9 a (21 b)}{7 b^{3} (12 a^{2})}$

$\frac{9 a (21 b)}{7 b^{3} (12 a^{2})}$

Step 3.2

Cancel the common factor of $9$ and $12$ .

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Step 3.2.1

Factor $3$ out of $9 a (21 b)$ .

$\frac{3 (3 a (21 b))}{7 b^{3} (12 a^{2})}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $3$ out of $7 b^{3} (12 a^{2})$ .

$\frac{3 (3 a (21 b))}{3 (7 b^{3} (4 a^{2}))}$

Step 3.2.2.2

Cancel the common factor.

$\frac{3 (3 a (21 b))}{3 (7 b^{3} (4 a^{2}))}$

Step 3.2.2.3

Rewrite the expression.

$\frac{3 a (21 b)}{7 b^{3} (4 a^{2})}$

$\frac{3 a (21 b)}{7 b^{3} (4 a^{2})}$

$\frac{3 a (21 b)}{7 b^{3} (4 a^{2})}$

Step 3.3

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

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Step 3.3.1

Factor $a$ out of $3 a (21 b)$ .

$\frac{a (3 (21 b))}{7 b^{3} (4 a^{2})}$

Step 3.3.2

Cancel the common factors.

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Step 3.3.2.1

Factor $a$ out of $7 b^{3} (4 a^{2})$ .

$\frac{a (3 (21 b))}{a (7 b^{3} (4 a))}$

Step 3.3.2.2

Cancel the common factor.

$\frac{a (3 (21 b))}{a (7 b^{3} (4 a))}$

Step 3.3.2.3

Rewrite the expression.

$\frac{3 (21 b)}{7 b^{3} (4 a)}$

$\frac{3 (21 b)}{7 b^{3} (4 a)}$

$\frac{3 (21 b)}{7 b^{3} (4 a)}$

Step 3.4

Cancel the common factor of $21$ and $7$ .

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Step 3.4.1

Factor $7$ out of $3 (21 b)$ .

$\frac{7 (3 (3 b))}{7 b^{3} (4 a)}$

Step 3.4.2

Cancel the common factors.

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Step 3.4.2.1

Factor $7$ out of $7 b^{3} (4 a)$ .

$\frac{7 (3 (3 b))}{7 (b^{3} (4 a))}$

Step 3.4.2.2

Cancel the common factor.

$\frac{7 (3 (3 b))}{7 (b^{3} (4 a))}$

Step 3.4.2.3

Rewrite the expression.

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

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

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

Step 3.5

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

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Step 3.5.1

Factor $b$ out of $3 (3 b)$ .

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

Step 3.5.2

Cancel the common factors.

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Step 3.5.2.1

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

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

Step 3.5.2.2

Cancel the common factor.

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

Step 3.5.2.3

Rewrite the expression.

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

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

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

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

Step 4

Multiply $3$ by $3$ .

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

Step 5

Move $4$ to the left of $b^{2}$ .

$\frac{9}{4 b^{2} a}$

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