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The value(s) of [tex]\((16)^{\frac{1}{4}}\)[/tex] is(are):

A. [tex]\(\pm 2\)[/tex]

B. 2

C. [tex]\(2i\)[/tex]

D. 4

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]