Basic Math Examples

$\frac{15 a^{4}}{21 b^{5}} \cdot (\frac{- 6 b}{21 a^{2}})$

Step 1

Combine.

$\frac{15 a^{4} (- 6 b)}{21 b^{5} (21 a^{2})}$

Step 2

Cancel the common factor of $15$ and $21$ .

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Step 2.1

Factor $3$ out of $15 a^{4} (- 6 b)$ .

$\frac{3 (5 a^{4} (- 6 b))}{21 b^{5} (21 a^{2})}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $3$ out of $21 b^{5} (21 a^{2})$ .

$\frac{3 (5 a^{4} (- 6 b))}{3 (7 b^{5} (21 a^{2}))}$

Step 2.2.2

Cancel the common factor.

$\frac{3 (5 a^{4} (- 6 b))}{3 (7 b^{5} (21 a^{2}))}$

Step 2.2.3

Rewrite the expression.

$\frac{5 a^{4} (- 6 b)}{7 b^{5} (21 a^{2})}$

Step 3

Cancel the common factor of $a^{4}$ and $a^{2}$ .

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Step 3.1

Factor $a^{2}$ out of $5 a^{4} (- 6 b)$ .

$\frac{a^{2} (5 a^{2} (- 6 b))}{7 b^{5} (21 a^{2})}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $a^{2}$ out of $7 b^{5} (21 a^{2})$ .

$\frac{a^{2} (5 a^{2} (- 6 b))}{a^{2} (7 b^{5} \cdot (21))}$

Step 3.2.2

Cancel the common factor.

$\frac{a^{2} (5 a^{2} (- 6 b))}{a^{2} (7 b^{5} \cdot (21))}$

Step 3.2.3

Rewrite the expression.

$\frac{5 a^{2} (- 6 b)}{7 b^{5} \cdot (21)}$

Step 4

Cancel the common factor of $- 6$ and $21$ .

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Step 4.1

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

$\frac{3 (5 a^{2} (- 2 b))}{7 b^{5} \cdot (21)}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $3$ out of $7 b^{5} \cdot (21)$ .

$\frac{3 (5 a^{2} (- 2 b))}{3 (7 b^{5} \cdot (7))}$

Step 4.2.2

Cancel the common factor.

$\frac{3 (5 a^{2} (- 2 b))}{3 (7 b^{5} \cdot (7))}$

Step 4.2.3

Rewrite the expression.

$\frac{5 a^{2} (- 2 b)}{7 b^{5} \cdot (7)}$

Step 5

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

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Step 5.1

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

$\frac{b (5 a^{2} \cdot (- 2))}{7 b^{5} \cdot (7)}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $b$ out of $7 b^{5} \cdot (7)$ .

$\frac{b (5 a^{2} \cdot (- 2))}{b (7 b^{4} \cdot 7)}$

Step 5.2.2

Cancel the common factor.

$\frac{b (5 a^{2} \cdot (- 2))}{b (7 b^{4} \cdot 7)}$

Step 5.2.3

Rewrite the expression.

$\frac{5 a^{2} \cdot (- 2)}{7 b^{4} \cdot 7}$

Step 6

Simplify the expression.

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Step 6.1

Multiply $- 2$ by $5$ .

$\frac{- 10 a^{2}}{7 b^{4} \cdot 7}$

Step 6.2

Multiply $7$ by $7$ .

$\frac{- 10 a^{2}}{49 b^{4}}$

Step 6.3

Move the negative in front of the fraction.

$- \frac{10 a^{2}}{49 b^{4}}$