Finite Math Examples

$\frac{(- \frac{4}{3} \cdot (a b)) (\frac{9}{4} \cdot (a^{2} b))}{{(- 2 a b)}^{2}}$

Step 1

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

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Step 1.1

Move $a^{2}$ .

$\frac{- \frac{4}{3} \cdot (a^{2} a b) (\frac{9}{4} \cdot (b))}{{(- 2 a b)}^{2}}$

Step 1.2

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

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Step 1.2.1

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

$\frac{- \frac{4}{3} \cdot (a^{2} a^{1} b) (\frac{9}{4} \cdot (b))}{{(- 2 a b)}^{2}}$

Step 1.2.2

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

$\frac{- \frac{4}{3} \cdot (a^{2 + 1} b) (\frac{9}{4} \cdot (b))}{{(- 2 a b)}^{2}}$

Step 1.3

Add $2$ and $1$ .

$\frac{- \frac{4}{3} \cdot (a^{3} b) (\frac{9}{4} \cdot (b))}{{(- 2 a b)}^{2}}$

Step 2

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

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Step 2.1

Move $b$ .

$\frac{- \frac{4}{3} \cdot (a^{3} (b \cdot b)) \frac{9}{4}}{{(- 2 a b)}^{2}}$

Step 2.2

Multiply $b$ by $b$ .

$\frac{- \frac{4}{3} \cdot (a^{3} b^{2}) \frac{9}{4}}{{(- 2 a b)}^{2}}$

Step 3

Simplify the numerator.

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Step 3.1

Combine $a^{3}$ and $\frac{4}{3}$ .

$\frac{- \frac{a^{3} \cdot 4}{3} b^{2} \frac{9}{4}}{{(- 2 a b)}^{2}}$

Step 3.2

Combine $b^{2}$ and $\frac{a^{3} \cdot 4}{3}$ .

$\frac{- \frac{b^{2} (a^{3} \cdot 4)}{3} \cdot \frac{9}{4}}{{(- 2 a b)}^{2}}$

Step 3.3

Multiply $\frac{9}{4}$ by $\frac{b^{2} (a^{3} \cdot 4)}{3}$ .

$\frac{- \frac{9 (b^{2} (a^{3} \cdot 4))}{4 \cdot 3}}{{(- 2 a b)}^{2}}$

Step 4

Simplify the denominator.

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Step 4.1

Apply the product rule to $- 2 a b$ .

$\frac{- \frac{9 (b^{2} (a^{3} \cdot 4))}{4 \cdot 3}}{{(- 2 a)}^{2} b^{2}}$

Step 4.2

Apply the product rule to $- 2 a$ .

$\frac{- \frac{9 (b^{2} (a^{3} \cdot 4))}{4 \cdot 3}}{{(- 2)}^{2} a^{2} b^{2}}$

Step 4.3

Raise $- 2$ to the power of $2$ .

$\frac{- \frac{9 (b^{2} (a^{3} \cdot 4))}{4 \cdot 3}}{4 a^{2} b^{2}}$

Step 5

Multiply $4$ by $9$ .

$\frac{- \frac{36 b^{2} a^{3}}{4 \cdot 3}}{4 a^{2} b^{2}}$

Step 6

Multiply $4$ by $3$ .

$\frac{- \frac{36 b^{2} a^{3}}{12}}{4 a^{2} b^{2}}$

Step 7

Simplify the numerator.

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Step 7.1

Reduce the expression by cancelling the common factors.

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Step 7.1.1

Reduce the expression $\frac{36 b^{2} a^{3}}{12}$ by cancelling the common factors.

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Step 7.1.1.1

Factor $12$ out of $36 b^{2} a^{3}$ .

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

Step 7.1.1.2

Factor $12$ out of $12$ .

$\frac{- \frac{12 (3 b^{2} a^{3})}{12 (1)}}{4 a^{2} b^{2}}$

Step 7.1.1.3

Cancel the common factor.

$\frac{- \frac{12 (3 b^{2} a^{3})}{12 \cdot 1}}{4 a^{2} b^{2}}$

Step 7.1.1.4

Rewrite the expression.

$\frac{- \frac{3 b^{2} a^{3}}{1}}{4 a^{2} b^{2}}$

Step 7.1.2

Divide $3 b^{2} a^{3}$ by $1$ .

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

$\frac{- 1 \cdot 3 b^{2} a^{3}}{4 a^{2} b^{2}}$

Step 7.2

Multiply $- 1$ by $3$ .

$\frac{- 3 b^{2} a^{3}}{4 a^{2} b^{2}}$

Step 8

Reduce the expression by cancelling the common factors.

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Step 8.1

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

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Step 8.1.1

Cancel the common factor.

$\frac{- 3 b^{2} a^{3}}{4 a^{2} b^{2}}$

Step 8.1.2

Rewrite the expression.

$\frac{- 3 a^{3}}{4 a^{2}}$

Step 8.2

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

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Step 8.2.1

Factor $a^{2}$ out of $- 3 a^{3}$ .

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

Step 8.2.2

Cancel the common factors.

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Step 8.2.2.1

Factor $a^{2}$ out of $4 a^{2}$ .

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

Step 8.2.2.2

Cancel the common factor.

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

Step 8.2.2.3

Rewrite the expression.

$\frac{- 3 a}{4}$

Step 8.3

Move the negative in front of the fraction.

$- \frac{3 a}{4}$