Finite Math Examples

${(\frac{1}{2})}^{2} {(1 - \frac{1}{2})}^{4 - 2}$

Step 1

Simplify the expression.

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Step 1.1

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

$\frac{1^{2}}{2^{2}} {(1 - \frac{1}{2})}^{4 - 2}$

Step 1.2

One to any power is one.

$\frac{1}{2^{2}} {(1 - \frac{1}{2})}^{4 - 2}$

Step 1.3

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

$\frac{1}{4} {(1 - \frac{1}{2})}^{4 - 2}$

Step 1.4

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

$\frac{1}{4} {(\frac{2}{2} - \frac{1}{2})}^{4 - 2}$

Step 1.5

Combine the numerators over the common denominator.

$\frac{1}{4} {(\frac{2 - 1}{2})}^{4 - 2}$

Step 1.6

Subtract $1$ from $2$ .

$\frac{1}{4} {(\frac{1}{2})}^{4 - 2}$

Step 1.7

Subtract $2$ from $4$ .

$\frac{1}{4} {(\frac{1}{2})}^{2}$

Step 1.8

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

$\frac{1}{4} \cdot \frac{1^{2}}{2^{2}}$

Step 2

Combine.

$\frac{1 \cdot 1^{2}}{4 \cdot 2^{2}}$

Step 3

Multiply $1$ by $1^{2}$ by adding the exponents.

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Step 3.1

Multiply $1$ by $1^{2}$ .

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Step 3.1.1

Raise $1$ to the power of $1$ .

$\frac{1^{1} \cdot 1^{2}}{4 \cdot 2^{2}}$

Step 3.1.2

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

$\frac{1^{1 + 2}}{4 \cdot 2^{2}}$

Step 3.2

Add $1$ and $2$ .

$\frac{1^{3}}{4 \cdot 2^{2}}$

Step 4

One to any power is one.

$\frac{1}{4 \cdot 2^{2}}$

Step 5

Simplify the denominator.

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Step 5.1

Rewrite $4$ as $2^{2}$ .

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

Step 5.2

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

$\frac{1}{2^{2 + 2}}$

Step 5.3

Add $2$ and $2$ .

$\frac{1}{2^{4}}$

Step 6

Raise $2$ to the power of $4$ .

$\frac{1}{16}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{16}$

Decimal Form:

$0.0625$