Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Experience the convenience of finding accurate answers to your questions from knowledgeable professionals on our platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

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]

Sagot :

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]
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.