CMA Foundation · Fundamentals of Business Mathematics and Statistics · Indices and Logarithms
Simplify: (27)^(2/3) × (16)^(-1/4) ÷ (9)^(1/2).
The expression equals 3/2. 27^(2/3) is 9, 16^(-1/4) is 1/2, and 9^(1/2) is 3, so the result is 9 × 1/2 ÷ 3 = 3/2.
- A3/2Correct
- B2/3
- C3
- D9/2
Explanation
27^(2/3) = (3^3)^(2/3) = 9. 16^(-1/4) = 1/2. 9^(1/2) = 3. So 9 × 1/2 ÷ 3 = 4.5 ÷ 3 = 3/2. Option 3 results from ignoring the negative index on 16, which would give 9×2÷3 = 6, not 3, so 3 is just wrong arithmetic.
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