Finite Math Examples

$\frac{2^{n + 4} - 2 \cdot 2^{n}}{2^{n + 2} \cdot 4}$

Step 1

Multiply $- 2 \cdot 2^{n}$ .

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Step 1.1

Factor out negative.

$\frac{2^{n + 4} - (2 \cdot 2^{n})}{2^{n + 2} \cdot 4}$

Step 1.2

Raise $2$ to the power of $1$ .

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

Step 1.3

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

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

Step 2

Simplify the denominator.

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Step 2.1

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

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

Step 2.2

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

$\frac{2^{n + 4} - 2^{1 + n}}{2^{n + 2 + 2}}$

Step 2.3

Add $2$ and $2$ .

$\frac{2^{n + 4} - 2^{1 + n}}{2^{n + 4}}$

Step 3

Split the fraction $\frac{2^{n + 4} - 2^{1 + n}}{2^{n + 4}}$ into two fractions.

$\frac{2^{n + 4}}{2^{n + 4}} + \frac{- 2^{1 + n}}{2^{n + 4}}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Cancel the common factor of $2^{n + 4}$ .

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Step 4.1.1

Cancel the common factor.

$\frac{2^{n + 4}}{2^{n + 4}} + \frac{- 2^{1 + n}}{2^{n + 4}}$

Step 4.1.2

Rewrite the expression.

$1 + \frac{- 2^{1 + n}}{2^{n + 4}}$

Step 4.2

Cancel the common factor of $2^{1 + n}$ and $2^{n + 4}$ .

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Step 4.2.1

Factor $2^{n + 4}$ out of $- 2^{1 + n}$ .

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

Step 4.2.2

Cancel the common factors.

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Step 4.2.2.1

Multiply by $1$ .

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

Step 4.2.2.2

Cancel the common factor.

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

Step 4.2.2.3

Rewrite the expression.

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

Step 4.2.2.4

Divide $- 2^{1 + n - (n + 4)}$ by $1$ .

$1 - 2^{1 + n - (n + 4)}$

Step 5

Simplify each term.

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Step 5.1

Apply the distributive property.

$1 - 2^{1 + n - n - 1 \cdot 4}$

Step 5.2

Multiply $- 1$ by $4$ .

$1 - 2^{1 + n - n - 4}$

Step 6

Simplify by adding terms.

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Step 6.1

Combine the opposite terms in $1 + n - n - 4$ .

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Step 6.1.1

Subtract $n$ from $n$ .

$1 - 2^{1 + 0 - 4}$

Step 6.1.2

Add $1$ and $0$ .

$1 - 2^{1 - 4}$

Step 6.2

Subtract $4$ from $1$ .

$1 - 2^{- 3}$

Step 7

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$1 - \frac{1}{2^{3}}$

Step 8

Raise $2$ to the power of $3$ .

$1 - \frac{1}{8}$

Step 9

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

$\frac{8}{8} - \frac{1}{8}$

Step 10

Combine the numerators over the common denominator.

$\frac{8 - 1}{8}$

Step 11

Subtract $1$ from $8$ .

$\frac{7}{8}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{8}$

Decimal Form:

$0.875$