Solve for S S=(2^(x-1)+2^(x-2))*2^(-x+2)

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

Apply the distributive property.

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

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

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

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

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

Subtract $x$ from $x$ .

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

Subtract $1$ from $0$ .

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

Add $- 1$ and $2$ .

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

Simplify $2^{1}$ .

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

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

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

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

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

Subtract $x$ from $x$ .

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

Subtract $2$ from $0$ .

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

Add $- 2$ and $2$ .

$S = 2 + 2^{0}$

Simplify $2^{0}$ .

$S = 2 + 1$

Add $2$ and $1$ .

$S = 3$