Finite Math Examples

$6000 {(1 + \frac{56}{6000})}^{72} = A$

Step 1

Rewrite the equation as $A = 6000 {(1 + \frac{56}{6000})}^{72}$ .

$A = 6000 {(1 + \frac{56}{6000})}^{72}$

Step 2

Simplify $6000 {(1 + \frac{56}{6000})}^{72}$ .

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Step 2.1

Cancel the common factor of $56$ and $6000$ .

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Step 2.1.1

Factor $8$ out of $56$ .

$A = 6000 {(1 + \frac{8 (7)}{6000})}^{72}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $8$ out of $6000$ .

$A = 6000 {(1 + \frac{8 \cdot 7}{8 \cdot 750})}^{72}$

Step 2.1.2.2

Cancel the common factor.

$A = 6000 {(1 + \frac{8 \cdot 7}{8 \cdot 750})}^{72}$

Step 2.1.2.3

Rewrite the expression.

$A = 6000 {(1 + \frac{7}{750})}^{72}$

Step 2.2

Simplify the expression.

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Step 2.2.1

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

$A = 6000 {(\frac{750}{750} + \frac{7}{750})}^{72}$

Step 2.2.2

Combine the numerators over the common denominator.

$A = 6000 {(\frac{750 + 7}{750})}^{72}$

Step 2.2.3

Add $750$ and $7$ .

$A = 6000 {(\frac{757}{750})}^{72}$

Step 2.2.4

Apply the product rule to $\frac{757}{750}$ .

$A = 6000 \frac{757^{72}}{750^{72}}$

Step 2.3

Combine $6000$ and $\frac{757^{72}}{750^{72}}$ .

$A = \frac{6000 \cdot 757^{72}}{750^{72}}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$A = \frac{6000 \cdot 757^{72}}{750^{72}}$

Decimal Form:

$A = 11712.33835660 \dots$