Finite Math Examples

$47000 {(1 + \frac{\frac{93}{4}}{4})}^{20}$

Step 1

Simplify each term.

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Step 1.1

Multiply the numerator by the reciprocal of the denominator.

$47000 {(1 + \frac{93}{4} \cdot \frac{1}{4})}^{20}$

Step 1.2

Multiply $\frac{93}{4} \cdot \frac{1}{4}$ .

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Step 1.2.1

Multiply $\frac{93}{4}$ by $\frac{1}{4}$ .

$47000 {(1 + \frac{93}{4 \cdot 4})}^{20}$

Step 1.2.2

Multiply $4$ by $4$ .

$47000 {(1 + \frac{93}{16})}^{20}$

Step 2

Simplify terms.

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Step 2.1

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

$47000 {(\frac{16}{16} + \frac{93}{16})}^{20}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Combine the numerators over the common denominator.

$47000 {(\frac{16 + 93}{16})}^{20}$

Step 2.2.2

Add $16$ and $93$ .

$47000 {(\frac{109}{16})}^{20}$

Step 2.2.3

Apply the product rule to $\frac{109}{16}$ .

$47000 \frac{109^{20}}{16^{20}}$

Step 2.2.4

Raise $16$ to the power of $20$ .

$47000 \frac{109^{20}}{1208925819614630000000000}$

Step 2.3

Cancel the common factor of $1000$ .

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Step 2.3.1

Factor $1000$ out of $47000$ .

$1000 (47) \frac{109^{20}}{1208925819614630000000000}$

Step 2.3.2

Factor $1000$ out of $1208925819614630000000000$ .

$1000 \cdot 47 \frac{109^{20}}{1000 \cdot 1208925819614630000000}$

Step 2.3.3

Cancel the common factor.

$1000 \cdot 47 \frac{109^{20}}{1000 \cdot 1208925819614630000000}$

Step 2.3.4

Rewrite the expression.

$47 \frac{109^{20}}{1208925819614630000000}$

Step 2.4

Combine $47$ and $\frac{109^{20}}{1208925819614630000000}$ .

$\frac{47 \cdot 109^{20}}{1208925819614630000000}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{47 \cdot 109^{20}}{1208925819614630000000}$

Decimal Form:

$2.17885416 \cdot 10^{21}$