Advanced MathHardPower of a fractional power
Advanced Math practice question
For x > 0, which expression is equivalent to (x^(2/3))^(3/4)?
- A. √xCorrect
- B. x^(17/12)
- C. x^(8/9)
- D. x²
Answer: A. √x
A power of a power multiplies the exponents: (2/3)(3/4) = 6/12 = 1/2. So the expression is x^(1/2) = √x.
Why the other answers are wrong
- B. x^(17/12)
- 17/12 ADDS the exponents (2/3 + 3/4); a power of a power multiplies them.
- C. x^(8/9)
- 8/9 DIVIDES 2/3 by 3/4; multiply instead.
- D. x²
- x² would need exponents multiplying to 2, but (2/3)(3/4) = 1/2.
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