Advanced MathMediumFractional exponent of a monomial
Advanced Math practice question
For x > 0, which expression is equivalent to (16x⁸)^(1/4)?
- A. 2x²Correct
- B. 4x²
- C. 2x⁴
- D. 4x⁴
Answer: A. 2x²
The fourth root applies to each factor: 16^(1/4) = 2 and (x⁸)^(1/4) = x^(8/4) = x². So the expression is 2x².
Why the other answers are wrong
- B. 4x²
- 4 is the square root of 16, not the fourth root.
- C. 2x⁴
- x⁴ halves the exponent 8 instead of dividing it by 4.
- D. 4x⁴
- Both the coefficient and the exponent were treated as square roots.
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