Basic Math Examples

$\frac{- 3 a}{7 b} \cdot \frac{7 a b}{2 b} \cdot \frac{9 a b}{5 b}$

Step 1

Cancel the common factor of $7 b$ .

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Step 1.1

Factor $7 b$ out of $7 a b$ .

$\frac{- 3 a}{7 b} \cdot \frac{7 b (a)}{2 b} \cdot \frac{9 a b}{5 b}$

Step 1.2

Cancel the common factor.

$\frac{- 3 a}{7 b} \cdot \frac{7 b a}{2 b} \cdot \frac{9 a b}{5 b}$

Step 1.3

Rewrite the expression.

$- 3 a \cdot \frac{a}{2 b} \cdot \frac{9 a b}{5 b}$

Step 2

Combine $- 3$ and $\frac{a}{2 b}$ .

$a \cdot \frac{- 3 a}{2 b} \cdot \frac{9 a b}{5 b}$

Step 3

Combine $a$ and $\frac{- 3 a}{2 b}$ .

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

Step 4

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

$\frac{- 3 (a^{1} a)}{2 b} \cdot \frac{9 a b}{5 b}$

Step 5

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

$\frac{- 3 (a^{1} a^{1})}{2 b} \cdot \frac{9 a b}{5 b}$

Step 6

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

$\frac{- 3 a^{1 + 1}}{2 b} \cdot \frac{9 a b}{5 b}$

Step 7

Add $1$ and $1$ .

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

Step 8

Combine.

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

Step 9

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

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Step 9.1

Move $a$ .

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

Step 9.2

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

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Step 9.2.1

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

$\frac{- 3 (a^{1} a^{2}) (9 b)}{2 b (5 b)}$

Step 9.2.2

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

$\frac{- 3 a^{1 + 2} (9 b)}{2 b (5 b)}$

Step 9.3

Add $1$ and $2$ .

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

Step 10

Multiply $b$ by $b$ by adding the exponents.

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Step 10.1

Move $b$ .

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

Step 10.2

Multiply $b$ by $b$ .

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

Step 11

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

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Step 11.1

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

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

Step 11.2

Cancel the common factors.

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Step 11.2.1

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

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

Step 11.2.2

Cancel the common factor.

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

Step 11.2.3

Rewrite the expression.

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

Step 12

Simplify the expression.

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Step 12.1

Multiply $9$ by $- 3$ .

$\frac{- 27 a^{3}}{2 b \cdot 5}$

Step 12.2

Multiply $5$ by $2$ .

$\frac{- 27 a^{3}}{10 b}$

Step 12.3

Move the negative in front of the fraction.

$- \frac{27 a^{3}}{10 b}$