Finite Math Examples

$5 C^{4} {(\frac{1}{2})}^{4} (1 - \frac{1}{2^{\frac{5}{4}}})$

Step 1

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

$5 C^{4} \frac{1^{4}}{2^{4}} (1 - \frac{1}{2^{\frac{5}{4}}})$

Step 2

One to any power is one.

$5 C^{4} \frac{1}{2^{4}} (1 - \frac{1}{2^{\frac{5}{4}}})$

Step 3

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

$5 C^{4} \frac{1}{16} (1 - \frac{1}{2^{\frac{5}{4}}})$

Step 4

Multiply $5 C^{4} \frac{1}{16}$ .

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Step 4.1

Combine $5$ and $\frac{1}{16}$ .

$C^{4} \frac{5}{16} (1 - \frac{1}{2^{\frac{5}{4}}})$

Step 4.2

Combine $C^{4}$ and $\frac{5}{16}$ .

$\frac{C^{4} \cdot 5}{16} (1 - \frac{1}{2^{\frac{5}{4}}})$

Step 5

Move $5$ to the left of $C^{4}$ .

$\frac{5 \cdot C^{4}}{16} (1 - \frac{1}{2^{\frac{5}{4}}})$

Step 6

Apply the distributive property.

$\frac{5 C^{4}}{16} \cdot 1 + \frac{5 C^{4}}{16} (- \frac{1}{2^{\frac{5}{4}}})$

Step 7

Multiply $\frac{5 C^{4}}{16}$ by $1$ .

$\frac{5 C^{4}}{16} + \frac{5 C^{4}}{16} (- \frac{1}{2^{\frac{5}{4}}})$

Step 8

Multiply $\frac{5 C^{4}}{16} (- \frac{1}{2^{\frac{5}{4}}})$ .

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Step 8.1

Multiply $\frac{5 C^{4}}{16}$ by $\frac{1}{2^{\frac{5}{4}}}$ .

$\frac{5 C^{4}}{16} - \frac{5 C^{4}}{16 \cdot 2^{\frac{5}{4}}}$

Step 8.2

Rewrite $16$ as $2^{4}$ .

$\frac{5 C^{4}}{16} - \frac{5 C^{4}}{2^{4} \cdot 2^{\frac{5}{4}}}$

Step 8.3

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

$\frac{5 C^{4}}{16} - \frac{5 C^{4}}{2^{4 + \frac{5}{4}}}$

Step 8.4

To write $4$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{5 C^{4}}{16} - \frac{5 C^{4}}{2^{4 \cdot \frac{4}{4} + \frac{5}{4}}}$

Step 8.5

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

$\frac{5 C^{4}}{16} - \frac{5 C^{4}}{2^{\frac{4 \cdot 4}{4} + \frac{5}{4}}}$

Step 8.6

Combine the numerators over the common denominator.

$\frac{5 C^{4}}{16} - \frac{5 C^{4}}{2^{\frac{4 \cdot 4 + 5}{4}}}$

Step 8.7

Simplify the numerator.

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Step 8.7.1

Multiply $4$ by $4$ .

$\frac{5 C^{4}}{16} - \frac{5 C^{4}}{2^{\frac{16 + 5}{4}}}$

Step 8.7.2

Add $16$ and $5$ .

$\frac{5 C^{4}}{16} - \frac{5 C^{4}}{2^{\frac{21}{4}}}$