Finite Math Examples

$p = \frac{188000 (\frac{0.0735}{10})}{1 - {(\frac{1 (0.0735)}{10})}^{- 300}}$

Step 1

Combine fractions.

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Step 1.1

Multiply $0.0735$ by $1$ .

$p = \frac{188000 (\frac{0.0735}{10})}{1 - {(\frac{0.0735}{10})}^{- 300}}$

Step 1.2

Combine $188000$ and $\frac{0.0735}{10}$ .

$p = \frac{\frac{188000 \cdot 0.0735}{10}}{1 - {(\frac{0.0735}{10})}^{- 300}}$

Step 2

Simplify the denominator.

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Step 2.1

Divide $0.0735$ by $10$ .

$p = \frac{\frac{188000 \cdot 0.0735}{10}}{1 - {0.00735}^{- 300}}$

Step 2.2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$p = \frac{\frac{188000 \cdot 0.0735}{10}}{1 - \frac{1}{{0.00735}^{300}}}$

Step 2.3

Write $1$ as a fraction with a common denominator.

$p = \frac{\frac{188000 \cdot 0.0735}{10}}{\frac{{0.00735}^{300}}{{0.00735}^{300}} - \frac{1}{{0.00735}^{300}}}$

Step 2.4

Combine the numerators over the common denominator.

$p = \frac{\frac{188000 \cdot 0.0735}{10}}{\frac{{0.00735}^{300} - 1}{{0.00735}^{300}}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Multiply $188000$ by $0.0735$ .

$p = \frac{\frac{13818}{10}}{\frac{{0.00735}^{300} - 1}{{0.00735}^{300}}}$

Step 3.2

Cancel the common factor of $13818$ and $10$ .

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Step 3.2.1

Factor $2$ out of $13818$ .

$p = \frac{\frac{2 (6909)}{10}}{\frac{{0.00735}^{300} - 1}{{0.00735}^{300}}}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $2$ out of $10$ .

$p = \frac{\frac{2 \cdot 6909}{2 \cdot 5}}{\frac{{0.00735}^{300} - 1}{{0.00735}^{300}}}$

Step 3.2.2.2

Cancel the common factor.

$p = \frac{\frac{2 \cdot 6909}{2 \cdot 5}}{\frac{{0.00735}^{300} - 1}{{0.00735}^{300}}}$

Step 3.2.2.3

Rewrite the expression.

$p = \frac{\frac{6909}{5}}{\frac{{0.00735}^{300} - 1}{{0.00735}^{300}}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$p = \frac{6909}{5} \cdot \frac{{0.00735}^{300}}{{0.00735}^{300} - 1}$

Step 5

Multiply $\frac{6909}{5}$ by $\frac{{0.00735}^{300}}{{0.00735}^{300} - 1}$ .

$p = \frac{6909 \cdot {0.00735}^{300}}{5 ({0.00735}^{300} - 1)}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$p = \frac{6909 \cdot {0.00735}^{300}}{5 ({0.00735}^{300} - 1)}$

Decimal Form:

$p = 0$