Algebra Examples

$S = (2^{x - 1} + 2^{x - 2}) \cdot 2^{- x + 2}$

Step 1

Apply the distributive property.

$S = 2^{x - 1} \cdot 2^{- x + 2} + 2^{x - 2} \cdot 2^{- x + 2}$

Step 2

Multiply $2^{x - 1}$ by $2^{- x + 2}$ by adding the exponents.

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Step 2.1

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

$S = 2^{x - 1 - x + 2} + 2^{x - 2} \cdot 2^{- x + 2}$

Step 2.2

Combine the opposite terms in $x - 1 - x + 2$ .

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Step 2.2.1

Subtract $x$ from $x$ .

$S = 2^{0 - 1 + 2} + 2^{x - 2} \cdot 2^{- x + 2}$

Step 2.2.2

Subtract $1$ from $0$ .

$S = 2^{- 1 + 2} + 2^{x - 2} \cdot 2^{- x + 2}$

Step 2.3

Add $- 1$ and $2$ .

$S = 2^{1} + 2^{x - 2} \cdot 2^{- x + 2}$

Step 3

Simplify $2^{1}$ .

$S = 2 + 2^{x - 2} \cdot 2^{- x + 2}$

Step 4

Multiply $2^{x - 2}$ by $2^{- x + 2}$ by adding the exponents.

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Step 4.1

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

$S = 2 + 2^{x - 2 - x + 2}$

Step 4.2

Combine the opposite terms in $x - 2 - x + 2$ .

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Step 4.2.1

Subtract $x$ from $x$ .

$S = 2 + 2^{0 - 2 + 2}$

Step 4.2.2

Subtract $2$ from $0$ .

$S = 2 + 2^{- 2 + 2}$

Step 4.2.3

Add $- 2$ and $2$ .

$S = 2 + 2^{0}$

Step 5

Simplify $2^{0}$ .

$S = 2 + 1$

Step 6

Add $2$ and $1$ .

$S = 3$