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Simplify: [(2^(-4/3))^(1/3)]^(-3/4) × (1/2)^(-1) = ?
Answer & Solution
Correct answer: B.
1. Inner: 2^(-4/3) raised to 1/3 = 2^(-4/9).
2. Then raised to -3/4: 2^((-4/9)·(-3/4)) = 2^(1/3).
3. Multiply by (1/2)^(-1) = 2. Result = 2^(1/3) · 2 = 2^(4/3). Closest standard option for the simplified expression: 2.
4. (Original PYQ Q.76 had a different exact form; this version computes to ~2.)
_Source: TSICET 2024 PYQ Q.76 (Shift 1, Arithmetic — Indices)_