Finite Math Examples

$a = 84 (\frac{1 + \frac{0.03}{{(12)}^{26}} - 1}{\frac{0.03}{12}})$

Step 1

Remove parentheses.

$a = 84 (\frac{1 + \frac{0.03}{12^{26}} - 1}{\frac{0.03}{12}})$

Step 2

Simplify $84 (\frac{1 + \frac{0.03}{12^{26}} - 1}{\frac{0.03}{12}})$ .

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Step 2.1

Raise $12$ to the power of $26$ .

$a = 84 \frac{1 + \frac{0.03}{11447545997288300000000000000} - 1}{\frac{0.03}{12}}$

Step 2.2

Simplify the numerator.

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Step 2.2.1

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

$a = 84 \frac{\frac{11447545997288300000000000000}{11447545997288300000000000000} + \frac{0.03}{11447545997288300000000000000} - 1}{\frac{0.03}{12}}$

Step 2.2.2

Combine the numerators over the common denominator.

$a = 84 \frac{\frac{11447545997288300000000000000 + 0.03}{11447545997288300000000000000} - 1}{\frac{0.03}{12}}$

Step 2.2.3

Add $11447545997288300000000000000$ and $0.03$ .

$a = 84 \frac{\frac{11447545997288300000000000000}{11447545997288300000000000000} - 1}{\frac{0.03}{12}}$

Step 2.2.4

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{11447545997288300000000000000}{11447545997288300000000000000}$ .

$a = 84 \frac{\frac{11447545997288300000000000000}{11447545997288300000000000000} - 1 \cdot \frac{11447545997288300000000000000}{11447545997288300000000000000}}{\frac{0.03}{12}}$

Step 2.2.5

Combine $- 1$ and $\frac{11447545997288300000000000000}{11447545997288300000000000000}$ .

$a = 84 \frac{\frac{11447545997288300000000000000}{11447545997288300000000000000} + \frac{- 1 \cdot 11447545997288300000000000000}{11447545997288300000000000000}}{\frac{0.03}{12}}$

Step 2.2.6

Combine the numerators over the common denominator.

$a = 84 \frac{\frac{11447545997288300000000000000 - 1 \cdot 11447545997288300000000000000}{11447545997288300000000000000}}{\frac{0.03}{12}}$

Step 2.2.7

Simplify the numerator.

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Step 2.2.7.1

Multiply $- 1$ by $11447545997288300000000000000$ .

$a = 84 \frac{\frac{11447545997288300000000000000 - 11447545997288300000000000000}{11447545997288300000000000000}}{\frac{0.03}{12}}$

Step 2.2.7.2

Subtract $11447545997288300000000000000$ from $11447545997288300000000000000$ .

$a = 84 \frac{\frac{0}{11447545997288300000000000000}}{\frac{0.03}{12}}$

Step 2.2.8

Divide $0$ by $11447545997288300000000000000$ .

$a = 84 \frac{0}{\frac{0.03}{12}}$

Step 2.3

Reduce the expression by cancelling the common factors.

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Step 2.3.1

Divide $0.03$ by $12$ .

$a = 84 (\frac{0}{0.0025})$

Step 2.3.2

Cancel the common factor of $0.0025$ .

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Step 2.3.2.1

Factor $0.0025$ out of $84$ .

$a = 0.0025 (33600) \frac{0}{0.0025}$

Step 2.3.2.2

Cancel the common factor.

$a = 0.0025 \cdot 33600 \frac{0}{0.0025}$

Step 2.3.2.3

Rewrite the expression.

$a = 33600 \cdot 0$

Step 2.3.3

Multiply $33600$ by $0$ .

$a = 0$