Finite Math Examples

$\frac{99 ({(- \frac{4}{3})}^{3} - 1)}{- \frac{4}{3} - 1}$

Step 1

Simplify the numerator.

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Step 1.1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1.1

Apply the product rule to $- \frac{4}{3}$ .

$\frac{99 ({(- 1)}^{3} {(\frac{4}{3})}^{3} - 1)}{- \frac{4}{3} - 1}$

Step 1.1.2

Apply the product rule to $\frac{4}{3}$ .

$\frac{99 ({(- 1)}^{3} \frac{4^{3}}{3^{3}} - 1)}{- \frac{4}{3} - 1}$

Step 1.2

Raise $- 1$ to the power of $3$ .

$\frac{99 (- \frac{4^{3}}{3^{3}} - 1)}{- \frac{4}{3} - 1}$

Step 1.3

Raise $4$ to the power of $3$ .

$\frac{99 (- \frac{64}{3^{3}} - 1)}{- \frac{4}{3} - 1}$

Step 1.4

Raise $3$ to the power of $3$ .

$\frac{99 (- \frac{64}{27} - 1)}{- \frac{4}{3} - 1}$

Step 1.5

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{27}{27}$ .

$\frac{99 (- \frac{64}{27} - 1 \cdot \frac{27}{27})}{- \frac{4}{3} - 1}$

Step 1.6

Combine $- 1$ and $\frac{27}{27}$ .

$\frac{99 (- \frac{64}{27} + \frac{- 1 \cdot 27}{27})}{- \frac{4}{3} - 1}$

Step 1.7

Combine the numerators over the common denominator.

$\frac{99 \frac{- 64 - 1 \cdot 27}{27}}{- \frac{4}{3} - 1}$

Step 1.8

Simplify the numerator.

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Step 1.8.1

Multiply $- 1$ by $27$ .

$\frac{99 \frac{- 64 - 27}{27}}{- \frac{4}{3} - 1}$

Step 1.8.2

Subtract $27$ from $- 64$ .

$\frac{99 (\frac{- 91}{27})}{- \frac{4}{3} - 1}$

Step 1.9

Move the negative in front of the fraction.

$\frac{99 \cdot - 1 \frac{91}{27}}{- \frac{4}{3} - 1}$

Step 1.10

Combine exponents.

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Step 1.10.1

Factor out negative.

$\frac{- (99 (\frac{91}{27}))}{- \frac{4}{3} - 1}$

Step 1.10.2

Combine $99$ and $\frac{91}{27}$ .

$\frac{- \frac{99 \cdot 91}{27}}{- \frac{4}{3} - 1}$

Step 1.10.3

Multiply $99$ by $91$ .

$\frac{- \frac{9009}{27}}{- \frac{4}{3} - 1}$

Step 1.11

Cancel the common factor of $9009$ and $27$ .

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Step 1.11.1

Factor $9$ out of $9009$ .

$\frac{- \frac{9 (1001)}{27}}{- \frac{4}{3} - 1}$

Step 1.11.2

Cancel the common factors.

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Step 1.11.2.1

Factor $9$ out of $27$ .

$\frac{- \frac{9 \cdot 1001}{9 \cdot 3}}{- \frac{4}{3} - 1}$

Step 1.11.2.2

Cancel the common factor.

$\frac{- \frac{9 \cdot 1001}{9 \cdot 3}}{- \frac{4}{3} - 1}$

Step 1.11.2.3

Rewrite the expression.

$\frac{- \frac{1001}{3}}{- \frac{4}{3} - 1}$

Step 2

Simplify the denominator.

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Step 2.1

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{- \frac{1001}{3}}{- \frac{4}{3} - 1 \cdot \frac{3}{3}}$

Step 2.2

Combine $- 1$ and $\frac{3}{3}$ .

$\frac{- \frac{1001}{3}}{- \frac{4}{3} + \frac{- 1 \cdot 3}{3}}$

Step 2.3

Combine the numerators over the common denominator.

$\frac{- \frac{1001}{3}}{\frac{- 4 - 1 \cdot 3}{3}}$

Step 2.4

Simplify the numerator.

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Step 2.4.1

Multiply $- 1$ by $3$ .

$\frac{- \frac{1001}{3}}{\frac{- 4 - 3}{3}}$

Step 2.4.2

Subtract $3$ from $- 4$ .

$\frac{- \frac{1001}{3}}{\frac{- 7}{3}}$

Step 2.5

Move the negative in front of the fraction.

$\frac{- \frac{1001}{3}}{- \frac{7}{3}}$

Step 3

Dividing two negative values results in a positive value.

$\frac{\frac{1001}{3}}{\frac{7}{3}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{1001}{3} \cdot \frac{3}{7}$

Step 5

Cancel the common factor of $7$ .

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Step 5.1

Factor $7$ out of $1001$ .

$\frac{7 (143)}{3} \cdot \frac{3}{7}$

Step 5.2

Cancel the common factor.

$\frac{7 \cdot 143}{3} \cdot \frac{3}{7}$

Step 5.3

Rewrite the expression.

$\frac{143}{3} \cdot 3$

Step 6

Cancel the common factor of $3$ .

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Step 6.1

Cancel the common factor.

$\frac{143}{3} \cdot 3$

Step 6.2

Rewrite the expression.

$143$