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If a = 3^(1/2), what is a^4?

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Question: If a = 3^(1/2), what is a^4?

Options:

  1. 9
  2. 27
  3. 81
  4. 3

Correct Answer: 81

Solution: 

a^4 = (3^(1/2))^4 = 3^2 = 9.

If a = 3^(1/2), what is a^4?

Practice Questions

Q1
If a = 3^(1/2), what is a^4?
  1. 9
  2. 27
  3. 81
  4. 3

Questions & Step-by-Step Solutions

If a = 3^(1/2), what is a^4?
Correct Answer: 9
  • Step 1: Start with the value of a, which is a = 3^(1/2).
  • Step 2: To find a^4, we need to calculate (3^(1/2))^4.
  • Step 3: Use the power of a power rule, which says (x^m)^n = x^(m*n).
  • Step 4: Apply the rule: (3^(1/2))^4 = 3^((1/2)*4).
  • Step 5: Calculate (1/2)*4, which equals 2.
  • Step 6: Now we have 3^2.
  • Step 7: Calculate 3^2, which is 3 * 3 = 9.
  • Exponents and Powers – Understanding how to manipulate exponents, including the rules for raising a power to another power.
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