Finite Math Examples

$3 C^{2} {(\frac{1}{2})}^{2} {(1 - \frac{1}{2})}^{3 - 2}$

Step 1

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

$3 C^{2} \frac{1^{2}}{2^{2}} {(1 - \frac{1}{2})}^{3 - 2}$

Step 2

One to any power is one.

$3 C^{2} \frac{1}{2^{2}} {(1 - \frac{1}{2})}^{3 - 2}$

Step 3

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

$3 C^{2} \frac{1}{4} {(1 - \frac{1}{2})}^{3 - 2}$

Step 4

Multiply $3 C^{2} \frac{1}{4}$ .

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Step 4.1

Combine $3$ and $\frac{1}{4}$ .

$C^{2} \frac{3}{4} {(1 - \frac{1}{2})}^{3 - 2}$

Step 4.2

Combine $C^{2}$ and $\frac{3}{4}$ .

$\frac{C^{2} \cdot 3}{4} {(1 - \frac{1}{2})}^{3 - 2}$

Step 5

Simplify the expression.

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Step 5.1

Move $3$ to the left of $C^{2}$ .

$\frac{3 \cdot C^{2}}{4} {(1 - \frac{1}{2})}^{3 - 2}$

Step 5.2

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

$\frac{3 C^{2}}{4} {(\frac{2}{2} - \frac{1}{2})}^{3 - 2}$

Step 5.3

Combine the numerators over the common denominator.

$\frac{3 C^{2}}{4} {(\frac{2 - 1}{2})}^{3 - 2}$

Step 5.4

Subtract $1$ from $2$ .

$\frac{3 C^{2}}{4} {(\frac{1}{2})}^{3 - 2}$

Step 5.5

Subtract $2$ from $3$ .

$\frac{3 C^{2}}{4} {(\frac{1}{2})}^{1}$

Step 5.6

Simplify.

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

Step 6

Combine.

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

Step 7

Multiply.

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Step 7.1

Multiply $3$ by $1$ .

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

Step 7.2

Multiply $4$ by $2$ .

$\frac{3 C^{2}}{8}$