CMA Foundation · Fundamentals of Business Mathematics and Statistics · Indices and Logarithms
The value of (27)^(2/3) × (16)^(-1/4) is:
The value is 9/2. Since 27^(2/3) = 3^2 = 9 and 16^(-1/4) = 1/2, because the negative power gives a reciprocal of the fourth root of 16, the product is 9 × 1/2 = 9/2. Ignoring the negative sign would wrongly give 18.
- A9/2Correct
- B3/2
- C18
- D9/4
Explanation
27^(2/3) = (3^3)^(2/3) = 3^2 = 9. 16^(-1/4) = 1/(2^4)^(1/4) = 1/2. The product is 9 × 1/2 = 9/2. Option 18 results from ignoring the negative sign and using 16^(1/4)=2.
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- Simplify: (27)^(2/3) × (16)^(-1/4) ÷ (9)^(1/2).