Evaluate f(x)=2(-2)^(3(-2)+4)

$f (x) = 2 {(- 2)}^{3 (- 2) + 4}$

Step 1

Simplify $2 {(- 2)}^{3 (- 2) + 4}$ .

Multiply $3$ by $- 2$ .

$f (x) = 2 {(- 2)}^{- 6 + 4}$

Add $- 6$ and $4$ .

$f (x) = 2 {(- 2)}^{- 2}$

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

$f (x) = 2 \frac{1}{{(- 2)}^{2}}$

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

$f (x) = 2 (\frac{1}{4})$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$f (x) = 2 \frac{1}{2 (2)}$

Cancel the common factor.

$f (x) = 2 \frac{1}{2 \cdot 2}$

Rewrite the expression.

$f (x) = \frac{1}{2}$

Step 2

Subtract $f (x)$ from both sides of the equation.

$0 = \frac{1}{2} - f (x)$

Step 3

Rewrite the equation as $\frac{1}{2} - f (x) = 0$ .

$\frac{1}{2} - f (x) = 0$