Advanced MathMediumPower of a power with a negative exponent
Advanced Math practice question
For x ≠ 0, which expression is equivalent to (x²)³ · x⁻²?
- A. x⁴Correct
- B. x³
- C. x⁸
- D. 1/x¹²
Answer: A. x⁴
(x²)³ = x⁶ (multiply the exponents). Then x⁶ · x⁻² = x⁶⁻² = x⁴ (add the exponents).
Why the other answers are wrong
- B. x³
- x³ comes from ADDING 2 and 3 for the power of a power (2 + 3 − 2). A power of a power multiplies: 2 × 3 = 6.
- C. x⁸
- x⁸ adds 2 instead of subtracting: the exponent is −2, so 6 + (−2) = 4.
- D. 1/x¹²
- 1/x¹² multiplies 6 by −2. Multiplying by x⁻² ADDS −2 to the exponent.
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