Evaluate 1/2-2^-4*4^2

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

Step 1

Simplify each term.

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

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

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

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

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

$\frac{1}{2} - \frac{1}{16} \cdot 16$

Cancel the common factor of $16$ .

Move the leading negative in $- \frac{1}{16}$ into the numerator.

$\frac{1}{2} + \frac{- 1}{16} \cdot 16$

Cancel the common factor.

$\frac{1}{2} + \frac{- 1}{16} \cdot 16$

Rewrite the expression.

$\frac{1}{2} - 1$

Step 2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 3

Combine $- 1$ and $\frac{2}{2}$ .

$\frac{1}{2} + \frac{- 1 \cdot 2}{2}$

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

Multiply $- 1$ by $2$ .

$\frac{1 - 2}{2}$

Subtract $2$ from $1$ .

$\frac{- 1}{2}$

Step 6

Move the negative in front of the fraction.

$- \frac{1}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{2}$

Decimal Form:

$- 0.5$