Question

question 22 of 25
evaluate: $2^{-4} =$

a. $-8$
b. $\frac{1}{16}$
c. $-16$
d. $\frac{1}{8}$

Explanation:

Step1: Recall negative exponent rule

The rule for negative exponents is \( a^{-n} = \frac{1}{a^{n}} \) where \( a
eq0 \) and \( n \) is a positive integer. For \( 2^{-4} \), we apply this rule.

Step2: Apply the rule and calculate

Using the rule, \( 2^{-4}=\frac{1}{2^{4}} \). Now, calculate \( 2^{4} = 2\times2\times2\times2 = 16 \). So, \( \frac{1}{2^{4}}=\frac{1}{16} \).

Answer:

B. \(\frac{1}{16}\)