CA Foundation · Quantitative Aptitude · Ratio and Proportion, Indices and Logarithms
The value of (81)^(3/4) × (8)^(−2/3) is:
The value is 27/4. Since 81 = 3^4, 81^(3/4) equals 3^3 = 27. Since 8 = 2^3, 8^(−2/3) equals 2^(−2) = 1/4. Multiplying 27 by 1/4 gives 27/4.
- A27/4Correct
- B9/4
- C27/2
- D3/4
Explanation
81^(3/4) = (3^4)^(3/4) = 3^3 = 27. 8^(−2/3) = (2^3)^(−2/3) = 2^(−2) = 1/4. The product is 27 × 1/4 = 27/4. Ignoring the negative sign would give 27×4 = 108, which is not an option, while 9/4 results from taking 81^(1/2).
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