Finite Math Examples

$s (- 8) = \frac{3 (1 - {(- 3)}^{- 8})}{1 - (- 3)}$

Step 1

Simplify.

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Step 1.1

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

$s (- 8) = \frac{3 (1 - \frac{1}{{(- 3)}^{8}})}{1 - (- 3)}$

Step 1.2

Raise $- 3$ to the power of $8$ .

$s (- 8) = \frac{3 (1 - \frac{1}{6561})}{1 - (- 3)}$

Step 1.3

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

$s (- 8) = \frac{3 (\frac{6561}{6561} - \frac{1}{6561})}{1 - (- 3)}$

Step 1.4

Combine the numerators over the common denominator.

$s (- 8) = \frac{3 \frac{6561 - 1}{6561}}{1 - (- 3)}$

Step 1.5

Subtract $1$ from $6561$ .

$s (- 8) = \frac{3 (\frac{6560}{6561})}{1 - (- 3)}$

Step 1.6

Cancel the common factor of $3$ .

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Step 1.6.1

Factor $3$ out of $6561$ .

$s (- 8) = \frac{3 \frac{6560}{3 (2187)}}{1 - (- 3)}$

Step 1.6.2

Cancel the common factor.

$s (- 8) = \frac{3 \frac{6560}{3 \cdot 2187}}{1 - (- 3)}$

Step 1.6.3

Rewrite the expression.

$s (- 8) = \frac{\frac{6560}{2187}}{1 - (- 3)}$

Step 1.7

Multiply $- 1$ by $- 3$ .

$s (- 8) = \frac{\frac{6560}{2187}}{1 + 3}$

Step 1.8

Multiply the numerator by the reciprocal of the denominator.

$s (- 8) = \frac{6560}{2187} \cdot \frac{1}{1 + 3}$

Step 1.9

Add $1$ and $3$ .

$s (- 8) = \frac{6560}{2187} \cdot \frac{1}{4}$

Step 1.10

Cancel the common factor of $4$ .

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Step 1.10.1

Factor $4$ out of $6560$ .

$s (- 8) = \frac{4 (1640)}{2187} \cdot \frac{1}{4}$

Step 1.10.2

Cancel the common factor.

$s (- 8) = \frac{4 \cdot 1640}{2187} \cdot \frac{1}{4}$

Step 1.10.3

Rewrite the expression.

$s (- 8) = \frac{1640}{2187}$

Step 2

Divide each term in $s (- 8) = \frac{1640}{2187}$ by $- 8$ and simplify.

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Step 2.1

Divide each term in $s (- 8) = \frac{1640}{2187}$ by $- 8$ .

$\frac{s (- 8)}{- 8} = \frac{\frac{1640}{2187}}{- 8}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 8$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{s \cdot - 8}{- 8} = \frac{\frac{1640}{2187}}{- 8}$

Step 2.2.1.2

Divide $s$ by $1$ .

$s = \frac{\frac{1640}{2187}}{- 8}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$s = \frac{1640}{2187} \cdot \frac{1}{- 8}$

Step 2.3.2

Cancel the common factor of $8$ .

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Step 2.3.2.1

Factor $8$ out of $1640$ .

$s = \frac{8 (205)}{2187} \cdot \frac{1}{- 8}$

Step 2.3.2.2

Factor $8$ out of $- 8$ .

$s = \frac{8 \cdot 205}{2187} \cdot \frac{1}{8 \cdot - 1}$

Step 2.3.2.3

Cancel the common factor.

$s = \frac{8 \cdot 205}{2187} \cdot \frac{1}{8 \cdot - 1}$

Step 2.3.2.4

Rewrite the expression.

$s = \frac{205}{2187} \cdot \frac{1}{- 1}$

Step 2.3.3

Multiply $\frac{205}{2187}$ by $\frac{1}{- 1}$ .

$s = \frac{205}{2187 \cdot - 1}$

Step 2.3.4

Simplify the expression.

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Step 2.3.4.1

Multiply $2187$ by $- 1$ .

$s = \frac{205}{- 2187}$

Step 2.3.4.2

Move the negative in front of the fraction.

$s = - \frac{205}{2187}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$s = - \frac{205}{2187}$

Decimal Form:

$s = - 0.09373571 \dots$