Finite Math Examples

16 C^{11} {(\frac{1}{2})}^{11} {(1 - \frac{1}{2})}^{16 - 11}

$16 C^{11} {(\frac{1}{2})}^{11} {(1 - \frac{1}{2})}^{16 - 11}$

Step 1

Simplify terms.

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Step 1.1

Apply the product rule to

\frac{1}{2}

$\frac{1}{2}$ .

16 C^{11} \frac{1^{11}}{2^{11}} {(1 - \frac{1}{2})}^{16 - 11}

$16 C^{11} \frac{1^{11}}{2^{11}} {(1 - \frac{1}{2})}^{16 - 11}$

Step 1.2

Simplify the expression.

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Step 1.2.1

One to any power is one.

16 C^{11} \frac{1}{2^{11}} {(1 - \frac{1}{2})}^{16 - 11}

$16 C^{11} \frac{1}{2^{11}} {(1 - \frac{1}{2})}^{16 - 11}$

Step 1.2.2

Raise

2

$2$ to the power of

11

$11$ .

16 C^{11} \frac{1}{2048} {(1 - \frac{1}{2})}^{16 - 11}

$16 C^{11} \frac{1}{2048} {(1 - \frac{1}{2})}^{16 - 11}$

16 C^{11} \frac{1}{2048} {(1 - \frac{1}{2})}^{16 - 11}

$16 C^{11} \frac{1}{2048} {(1 - \frac{1}{2})}^{16 - 11}$

Step 1.3

Cancel the common factor of

16

$16$ .

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Step 1.3.1

Factor

16

$16$ out of

16 C^{11}

$16 C^{11}$ .

16 (C^{11}) \frac{1}{2048} {(1 - \frac{1}{2})}^{16 - 11}

$16 (C^{11}) \frac{1}{2048} {(1 - \frac{1}{2})}^{16 - 11}$

Step 1.3.2

Factor

16

$16$ out of

2048

$2048$ .

16 (C^{11}) \frac{1}{16 (128)} {(1 - \frac{1}{2})}^{16 - 11}

$16 (C^{11}) \frac{1}{16 (128)} {(1 - \frac{1}{2})}^{16 - 11}$

Step 1.3.3

Cancel the common factor.

$16 C^{11} \frac{1}{16 \cdot 128} {(1 - \frac{1}{2})}^{16 - 11}$

Step 1.3.4

Rewrite the expression.

$C^{11} \frac{1}{128} {(1 - \frac{1}{2})}^{16 - 11}$

Step 1.4

Combine

$C^{11}$ and

$\frac{1}{128}$ .

$\frac{C^{11}}{128} {(1 - \frac{1}{2})}^{16 - 11}$

Step 1.5

Simplify the expression.

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Step 1.5.1

Write

$1$ as a fraction with a common denominator.

$\frac{C^{11}}{128} {(\frac{2}{2} - \frac{1}{2})}^{16 - 11}$

Step 1.5.2

Combine the numerators over the common denominator.

$\frac{C^{11}}{128} {(\frac{2 - 1}{2})}^{16 - 11}$

Step 1.5.3

Subtract

$1$ from

$2$ .

$\frac{C^{11}}{128} {(\frac{1}{2})}^{16 - 11}$

Step 1.5.4

Subtract

$11$ from

$16$ .

$\frac{C^{11}}{128} {(\frac{1}{2})}^{5}$

Step 1.5.5

Apply the product rule to

$\frac{1}{2}$ .

$\frac{C^{11}}{128} \cdot \frac{1^{5}}{2^{5}}$

Step 1.6

Combine.

$\frac{C^{11} \cdot 1^{5}}{128 \cdot 2^{5}}$

Step 1.7

One to any power is one.

$\frac{C^{11} \cdot 1}{128 \cdot 2^{5}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite

$128$ as

$2^{7}$ .

$\frac{C^{11} \cdot 1}{2^{7} \cdot 2^{5}}$

Step 2.2

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{C^{11} \cdot 1}{2^{7 + 5}}$

Step 2.3

Add

$7$ and

$5$ .

$\frac{C^{11} \cdot 1}{2^{12}}$

Step 3

Simplify the expression.

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Step 3.1

Multiply

$C^{11}$ by

$1$ .

$\frac{C^{11}}{2^{12}}$

Step 3.2

Raise

$2$ to the power of

$12$ .

$\frac{C^{11}}{4096}$