Certainly, let's analyze each of the given expressions and determine which one is equal to [tex]\(\frac{1}{16}\)[/tex].
First, let's evaluate the expression [tex]\(\left(\frac{1}{4}\right)^4\)[/tex]:
[tex]\[
\left(\frac{1}{4}\right)^4 = \left(\frac{1}{4} \times \frac{1}{4} \times \frac{1}{4} \times \frac{1}{4}\right) = \frac{1}{256}
\][/tex]
So, [tex]\(\left(\frac{1}{4}\right)^4\)[/tex] equals [tex]\(\frac{1}{256}\)[/tex], which is approximately 0.00390625.
Next, let's evaluate the expression [tex]\(\left(\frac{1}{8}\right)^2\)[/tex]:
[tex]\[
\left(\frac{1}{8}\right)^2 = \left(\frac{1}{8} \times \frac{1}{8}\right) = \frac{1}{64}
\][/tex]
So, [tex]\(\left(\frac{1}{8}\right)^2\)[/tex] equals [tex]\(\frac{1}{64}\)[/tex], which is approximately 0.015625.
Lastly, let's evaluate the expression [tex]\(\left(\frac{1}{2}\right)^4\)[/tex]:
[tex]\[
\left(\frac{1}{2}\right)^4 = \left(\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2}\right) = \frac{1}{16}
\][/tex]
So, [tex]\(\left(\frac{1}{2}\right)^4\)[/tex] equals [tex]\(\frac{1}{16}\)[/tex], which is 0.0625.
Among the three given expressions:
- [tex]\(\left(\frac{1}{4}\right)^4\)[/tex] equals [tex]\(\frac{1}{256}\)[/tex],
- [tex]\(\left(\frac{1}{8}\right)^2\)[/tex] equals [tex]\(\frac{1}{64}\)[/tex],
- [tex]\(\left(\frac{1}{2}\right)^4\)[/tex] equals [tex]\(\frac{1}{16}\)[/tex],
The correct option is [tex]\(\left(\frac{1}{2}\right)^4\)[/tex] which equals [tex]\(\frac{1}{16}\)[/tex].
