Algebra Examples

$S_{4} = \frac{1 (1 - {(\frac{1}{6})}^{4})}{1 - \frac{1}{6}}$

Step 1

Multiply $1 - {(\frac{1}{6})}^{4}$ by $1$ .

$S_{4} = \frac{1 - {(\frac{1}{6})}^{4}}{1 - \frac{1}{6}}$

Step 2

Simplify the denominator.

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

$S_{4} = \frac{1 - {(\frac{1}{6})}^{4}}{\frac{6}{6} - \frac{1}{6}}$

Combine the numerators over the common denominator.

$S_{4} = \frac{1 - {(\frac{1}{6})}^{4}}{\frac{6 - 1}{6}}$

Subtract $1$ from $6$ .

$S_{4} = \frac{1 - {(\frac{1}{6})}^{4}}{\frac{5}{6}}$

Step 3

Simplify the numerator.

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Apply the product rule to $\frac{1}{6}$ .

$S_{4} = \frac{1 - \frac{1^{4}}{6^{4}}}{\frac{5}{6}}$

One to any power is one.

$S_{4} = \frac{1 - \frac{1}{6^{4}}}{\frac{5}{6}}$

Raise $6$ to the power of $4$ .

$S_{4} = \frac{1 - \frac{1}{1296}}{\frac{5}{6}}$

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

$S_{4} = \frac{\frac{1296}{1296} - \frac{1}{1296}}{\frac{5}{6}}$

Combine the numerators over the common denominator.

$S_{4} = \frac{\frac{1296 - 1}{1296}}{\frac{5}{6}}$

Subtract $1$ from $1296$ .

$S_{4} = \frac{\frac{1295}{1296}}{\frac{5}{6}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$S_{4} = \frac{1295}{1296} \cdot \frac{6}{5}$

Step 5

Cancel the common factor of $5$ .

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Factor $5$ out of $1295$ .

$S_{4} = \frac{5 (259)}{1296} \cdot \frac{6}{5}$

Cancel the common factor.

$S_{4} = \frac{5 \cdot 259}{1296} \cdot \frac{6}{5}$

Rewrite the expression.

$S_{4} = \frac{259}{1296} \cdot 6$

Step 6

Cancel the common factor of $6$ .

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Factor $6$ out of $1296$ .

$S_{4} = \frac{259}{6 (216)} \cdot 6$

Cancel the common factor.

$S_{4} = \frac{259}{6 \cdot 216} \cdot 6$

Rewrite the expression.

$S_{4} = \frac{259}{216}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$S_{4} = \frac{259}{216}$

Decimal Form:

$S_{4} = 1.199\overline{074}$

Mixed Number Form:

$S_{4} = 1 \frac{43}{216}$