Finite Math Examples

$12870 {(\frac{1}{2})}^{8} \cdot {(1 - \frac{1}{2})}^{8}$

Step 1

Simplify terms.

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Step 1.1

Apply the product rule to $\frac{1}{2}$ .

$12870 \frac{1^{8}}{2^{8}} \cdot {(1 - \frac{1}{2})}^{8}$

Step 1.2

Simplify the expression.

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Step 1.2.1

One to any power is one.

$12870 \frac{1}{2^{8}} \cdot {(1 - \frac{1}{2})}^{8}$

Step 1.2.2

Raise $2$ to the power of $8$ .

$12870 (\frac{1}{256}) \cdot {(1 - \frac{1}{2})}^{8}$

Step 1.3

Cancel the common factor of $2$ .

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Step 1.3.1

Factor $2$ out of $12870$ .

$2 (6435) \frac{1}{256} \cdot {(1 - \frac{1}{2})}^{8}$

Step 1.3.2

Factor $2$ out of $256$ .

$2 \cdot 6435 \frac{1}{2 \cdot 128} \cdot {(1 - \frac{1}{2})}^{8}$

Step 1.3.3

Cancel the common factor.

$2 \cdot 6435 \frac{1}{2 \cdot 128} \cdot {(1 - \frac{1}{2})}^{8}$

Step 1.3.4

Rewrite the expression.

$6435 (\frac{1}{128}) \cdot {(1 - \frac{1}{2})}^{8}$

Step 1.4

Combine $6435$ and $\frac{1}{128}$ .

$\frac{6435}{128} \cdot {(1 - \frac{1}{2})}^{8}$

Step 1.5

Simplify the expression.

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Step 1.5.1

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

$\frac{6435}{128} \cdot {(\frac{2}{2} - \frac{1}{2})}^{8}$

Step 1.5.2

Combine the numerators over the common denominator.

$\frac{6435}{128} \cdot {(\frac{2 - 1}{2})}^{8}$

Step 1.5.3

Subtract $1$ from $2$ .

$\frac{6435}{128} \cdot {(\frac{1}{2})}^{8}$

Step 1.5.4

Apply the product rule to $\frac{1}{2}$ .

$\frac{6435}{128} \cdot \frac{1^{8}}{2^{8}}$

Step 1.6

Combine.

$\frac{6435 \cdot 1^{8}}{128 \cdot 2^{8}}$

Step 1.7

One to any power is one.

$\frac{6435 \cdot 1}{128 \cdot 2^{8}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $128$ as $2^{7}$ .

$\frac{6435 \cdot 1}{2^{7} \cdot 2^{8}}$

Step 2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{6435 \cdot 1}{2^{7 + 8}}$

Step 2.3

Add $7$ and $8$ .

$\frac{6435 \cdot 1}{2^{15}}$

Step 3

Simplify the expression.

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Step 3.1

Multiply $6435$ by $1$ .

$\frac{6435}{2^{15}}$

Step 3.2

Raise $2$ to the power of $15$ .

$\frac{6435}{32768}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{6435}{32768}$

Decimal Form:

$0.19638061 \dots$