Evaluate 1/4(2)^4-1/2(2)^2

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

Simplify each term.

Raise $2$ to the power of $4$ .

$\frac{1}{4} \cdot 16 - \frac{1}{2} \cdot {(2)}^{2}$

Cancel the common factor of $4$ .

Factor $4$ out of $16$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

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

Factor $2$ out of ${(2)}^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

$4 - 1 \cdot 2$

Multiply $- 1$ by $2$ .

$4 - 2$

Subtract $2$ from $4$ .

$2$