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Which of the following is equivalent to (x^(1/2))^4?

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Question: Which of the following is equivalent to (x^(1/2))^4?

Options:

  1. x^(2)
  2. x^(1)
  3. x^(1/4)
  4. x^(1/8)

Correct Answer: x^(2)

Solution: 

Using the power of a power property, (x^(1/2))^4 = x^(1/2 * 4) = x^(2).

Which of the following is equivalent to (x^(1/2))^4?

Practice Questions

Q1
Which of the following is equivalent to (x^(1/2))^4?
  1. x^(2)
  2. x^(1)
  3. x^(1/4)
  4. x^(1/8)

Questions & Step-by-Step Solutions

Which of the following is equivalent to (x^(1/2))^4?
Correct Answer: x^2
  • Step 1: Identify the expression we need to simplify, which is (x^(1/2))^4.
  • Step 2: Recall the power of a power property, which states that (a^m)^n = a^(m*n).
  • Step 3: Apply the power of a power property to our expression: (x^(1/2))^4 becomes x^((1/2)*4).
  • Step 4: Calculate (1/2) * 4, which equals 2.
  • Step 5: Substitute back into the expression: x^((1/2)*4) becomes x^2.
  • Step 6: Conclude that (x^(1/2))^4 is equivalent to x^2.
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