What is the value of (−1/512)⁻¹⁄³? (The exponent is −1/3.)
2021
What is the value of (−1/512)⁻¹⁄³? (The exponent is −1/3.)
- A.
4
- B.
-8
- C.
8
- D.
-4
Attempted by 33 students.
Show answer & explanation
Correct answer: B
Key idea: A negative exponent means take the reciprocal, and a cube root keeps the negative sign for a negative number.
Step 1: Rewrite the expression as (−1/512)^(−1/3).
Step 2: Using a negative exponent, (−1/512)^(−1/3) = (−512)^(1/3).
Step 3: Find the cube root: (−8)³ = −512, so (−512)^(1/3) = −8.
Final Answer: −8.