Evaluate negative fractional exponents and add: Compute (16)^(−3/4) + 2^(−3) + (8)^(−2/3).

Introduction / Context:This tests comfort with fractional and negative exponents. Using base-2 representations makes evaluation quick and exact without calculators.Given Data / Assumptions:

• (16)^(−3/4), 2^(−3), (8)^(−2/3).

Concept / Approach:Write 16 = 2^4 and 8 = 2^3, then apply (a^m)^n = a^(mn). Negative exponents give reciprocals: a^(−k) = 1/a^k.Step-by-Step Solution:

Verification / Alternative check:Compute as decimals: 0.125 + 0.125 + 0.25 = 0.5, which is 1/2.

Why Other Options Are Wrong:

• 3/2, 9/2, 5/4: Each implies at least one exponent was evaluated with the wrong sign or power.

Common Pitfalls:Confusing (a^m)^n with a^(m/n), or forgetting that negative exponents produce reciprocals.

Final Answer: