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

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

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

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



Answer :

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]