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If a^3 = b^2, which of the following is true?

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Question: If a^3 = b^2, which of the following is true?

Options:

  1. a = b^(2/3)
  2. b = a^(3/2)
  3. a^2 = b^(3/2)
  4. b^3 = a^2

Correct Answer: b = a^(3/2)

Solution: 

From a^3 = b^2, we can express b in terms of a as b = a^(3/2).

If a^3 = b^2, which of the following is true?

Practice Questions

Q1
If a^3 = b^2, which of the following is true?
  1. a = b^(2/3)
  2. b = a^(3/2)
  3. a^2 = b^(3/2)
  4. b^3 = a^2

Questions & Step-by-Step Solutions

If a^3 = b^2, which of the following is true?
  • Step 1: Start with the equation a^3 = b^2.
  • Step 2: To find b in terms of a, we need to isolate b.
  • Step 3: Take the square root of both sides of the equation. This gives us b = sqrt(a^3).
  • Step 4: Rewrite sqrt(a^3) as (a^3)^(1/2).
  • Step 5: Use the power of a power rule: (a^3)^(1/2) = a^(3/2).
  • Step 6: Therefore, we have b = a^(3/2).
  • Exponents and Powers – Understanding how to manipulate equations involving exponents to express one variable in terms of another.
  • Algebraic Manipulation – The ability to rearrange and solve equations to isolate variables.
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