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If x^4 = 81, what is the value of x?

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Question: If x^4 = 81, what is the value of x?

Options:

  1. 3
  2. 4
  3. 9
  4. 16

Correct Answer: 3

Solution: 

Taking the fourth root, x = 81^(1/4) = 3.

If x^4 = 81, what is the value of x?

Practice Questions

Q1
If x^4 = 81, what is the value of x?
  1. 3
  2. 4
  3. 9
  4. 16

Questions & Step-by-Step Solutions

If x^4 = 81, what is the value of x?
  • Step 1: Start with the equation x^4 = 81.
  • Step 2: To find x, we need to take the fourth root of both sides of the equation.
  • Step 3: The fourth root of x^4 is x, and the fourth root of 81 is written as 81^(1/4).
  • Step 4: Now we need to calculate 81^(1/4).
  • Step 5: We know that 81 is equal to 3^4, so we can rewrite it as (3^4)^(1/4).
  • Step 6: When we raise a power to a power, we multiply the exponents: 3^(4 * (1/4)) = 3^1.
  • Step 7: Therefore, x = 3.
  • Exponents and Roots – Understanding how to manipulate exponents and calculate roots, specifically the fourth root in this case.
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