Basic Math Examples

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

Step 1

Simplify the numerator.

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Step 1.1

Multiply $- 4 \cdot 2^{n - 2}$ .

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Step 1.1.1

Factor out negative.

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

Step 1.1.2

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

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

Step 1.1.3

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

$\frac{3 \cdot 2^{n} - 2^{2 + n - 2}}{2^{n} - 2^{n - 1}}$

Step 1.1.4

Subtract $2$ from $2$ .

$\frac{3 \cdot 2^{n} - 2^{n + 0}}{2^{n} - 2^{n - 1}}$

Step 1.1.5

Add $n$ and $0$ .

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

Step 1.2

Subtract $2^{n}$ from $3 \cdot 2^{n}$ .

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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