To determine which of the given expressions is equal to [tex]\(\frac{1}{16}\)[/tex], we need to evaluate each one individually.
1. Evaluating [tex]\(\left(\frac{1}{8}\right)^2\)[/tex]:
[tex]\[
\left(\frac{1}{8}\right)^2 = \frac{1}{8} \times \frac{1}{8} = \frac{1}{64}
\][/tex]
Since [tex]\(\frac{1}{64} \neq \frac{1}{16}\)[/tex], this expression is not equal to [tex]\(\frac{1}{16}\)[/tex].
2. Evaluating [tex]\(\left(\frac{1}{4}\right)^4\)[/tex]:
[tex]\[
\left(\frac{1}{4}\right)^4 = \frac{1}{4} \times \frac{1}{4} \times \frac{1}{4} \times \frac{1}{4} = \frac{1}{256}
\][/tex]
Since [tex]\(\frac{1}{256} \neq \frac{1}{16}\)[/tex], this expression is not equal to [tex]\(\frac{1}{16}\)[/tex].
3. Evaluating [tex]\(\left(\frac{1}{2}\right)^4\)[/tex]:
[tex]\[
\left(\frac{1}{2}\right)^4 = \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{16}
\][/tex]
Since [tex]\(\frac{1}{16} = \frac{1}{16}\)[/tex], this expression is equal to [tex]\(\frac{1}{16}\)[/tex].
Therefore, the expression that equals [tex]\(\frac{1}{16}\)[/tex] is:
[tex]\[
\left(\frac{1}{2}\right)^4
\][/tex]
