Which of the following expressions is equal to [tex]\( \frac{1}{16} \)[/tex]?

A. [tex]\( \left(\frac{1}{4}\right)^4 \)[/tex]

B. [tex]\( \left(\frac{1}{8}\right)^2 \)[/tex]

C. [tex]\( \left(\frac{1}{2}\right)^4 \)[/tex]



Answer :

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].