Evaluate Using Scientific Notation (-2^-4)^-2*(2^2)^0

${(- 2^{- 4})}^{- 2} \cdot {(2^{2})}^{0}$

Step 1

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

${(- \frac{1}{2^{4}})}^{- 2} \cdot {(2^{2})}^{0}$

Step 2

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

${(- \frac{1}{16})}^{- 2} \cdot {(2^{2})}^{0}$

Step 3

Change the sign of the exponent by rewriting the base as its reciprocal.

${(- 16)}^{2} \cdot {(2^{2})}^{0}$

Step 4

Raise $- 16$ to the power of $2$ .

$256 \cdot {(2^{2})}^{0}$

Step 5

Multiply the exponents in ${(2^{2})}^{0}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$256 \cdot 2^{2 \cdot 0}$

Multiply $2$ by $0$ .

$256 \cdot 2^{0}$

Step 6

Anything raised to $0$ is $1$ .

$256 \cdot 1$

Step 7

Multiply $256$ by $1$ .

$256$