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Which of the following is equal to 5^(2/3)?

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Question: Which of the following is equal to 5^(2/3)?

Options:

  1. √(25)
  2. 5√(5)
  3. 25
  4. √(125)

Correct Answer: 5√(5)

Solution: 

5^(2/3) = (5^(1/3))^2 = 5√(5).

Which of the following is equal to 5^(2/3)?

Practice Questions

Q1
Which of the following is equal to 5^(2/3)?
  1. √(25)
  2. 5√(5)
  3. 25
  4. √(125)

Questions & Step-by-Step Solutions

Which of the following is equal to 5^(2/3)?
Correct Answer: 5√(5)
  • Step 1: Understand that 5^(2/3) means 5 raised to the power of 2/3.
  • Step 2: Recognize that the exponent 2/3 can be split into two parts: the numerator (2) and the denominator (3).
  • Step 3: Rewrite 5^(2/3) as (5^(1/3))^2. This means we first take the cube root of 5 and then square it.
  • Step 4: Calculate 5^(1/3), which is the cube root of 5. We can write this as 5√(5).
  • Step 5: Now, square the result from Step 4. So, (5^(1/3))^2 = (5√(5))^2.
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