Discover a wealth of knowledge at Westonci.ca, where experts provide answers to your most pressing questions. Get immediate answers to your questions from a wide network of experienced professionals on our Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
To solve for the values of [tex]\( \left( 16 \right)^{\frac{1}{4}} \)[/tex], we need to determine the fourth roots of 16. Let's go through this step-by-step:
1. Understanding the Problem:
- We need to find the numbers which, when raised to the fourth power, give the value of 16.
- In mathematical form, we are searching for [tex]\( x \)[/tex] such that [tex]\( x^4 = 16 \)[/tex].
2. Identifying Possible Solutions:
- Let's consider both positive and negative numbers, since raising both a positive or a negative number to an even power will result in a positive number.
3. Positive Solution:
- Consider the number 2:
[tex]\[ 2^4 = 2 \times 2 \times 2 \times 2 = 16 \][/tex]
- So, 2 is one solution.
4. Negative Solution:
- Now consider the negative number -2:
[tex]\[ (-2)^4 = (-2) \times (-2) \times (-2) \times (-2) = 16 \][/tex]
- Because multiplying four negative twos results in a positive 16, -2 is also a solution.
5. Listing all Real Solutions:
- We have found that both 2 and -2 satisfy the equation [tex]\( x^4 = 16 \)[/tex]. Therefore, [tex]\( \pm 2 \)[/tex] are the real solutions.
6. Conclusion:
- The values of [tex]\( \left( 16 \right)^{\frac{1}{4}} \)[/tex] are [tex]\( \pm 2 \)[/tex].
Therefore, the correct answer to the question is:
A. [tex]\( \pm 2 \)[/tex]
1. Understanding the Problem:
- We need to find the numbers which, when raised to the fourth power, give the value of 16.
- In mathematical form, we are searching for [tex]\( x \)[/tex] such that [tex]\( x^4 = 16 \)[/tex].
2. Identifying Possible Solutions:
- Let's consider both positive and negative numbers, since raising both a positive or a negative number to an even power will result in a positive number.
3. Positive Solution:
- Consider the number 2:
[tex]\[ 2^4 = 2 \times 2 \times 2 \times 2 = 16 \][/tex]
- So, 2 is one solution.
4. Negative Solution:
- Now consider the negative number -2:
[tex]\[ (-2)^4 = (-2) \times (-2) \times (-2) \times (-2) = 16 \][/tex]
- Because multiplying four negative twos results in a positive 16, -2 is also a solution.
5. Listing all Real Solutions:
- We have found that both 2 and -2 satisfy the equation [tex]\( x^4 = 16 \)[/tex]. Therefore, [tex]\( \pm 2 \)[/tex] are the real solutions.
6. Conclusion:
- The values of [tex]\( \left( 16 \right)^{\frac{1}{4}} \)[/tex] are [tex]\( \pm 2 \)[/tex].
Therefore, the correct answer to the question is:
A. [tex]\( \pm 2 \)[/tex]
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.