CA Foundation · Quantitative Aptitude · Ratio and Proportion, Indices and Logarithms
Simplify: (a^(p) / a^(q))^(p+q) × (a^(q) / a^(r))^(q+r) × (a^(r) / a^(p))^(r+p)
The expression equals 1. Adding the exponents gives (p²−q²) + (q²−r²) + (r²−p²), which cancels to zero. Any non-zero base raised to the power zero equals 1, so the product is 1.
- A0
- Ba
- Ca^(p+q+r)
- D1Correct
Explanation
The exponent total is (p−q)(p+q) + (q−r)(q+r) + (r−p)(r+p) = (p²−q²) + (q²−r²) + (r²−p²) = 0. So the expression equals a^0 = 1. The option 0 confuses the exponent sum with the value of the expression.
Did you get it right without looking?
One question tells you little. A timed set on Ratio and Proportion, Indices and Logarithms shows your real accuracy, how long you take and where you lose marks.
More Ratio and Proportion, Indices and Logarithms questions
- The value of log₅ 125 + log₂ 32 − log₁₀ 1000 is:
- If a^x = b, b^y = c and c^z = a, where a, b, c are positive and different from 1, then the value of xyz is:
- The value of log₁₀ 0.001 is:
- The value of log₁₀ 5 + log₁₀ 20 is:
- If x varies directly as y and inversely as z, and x = 6 when y = 4 and z = 2, then the value of x when y = 9 and z = 6 is:
- If log₁₀ 2 = 0.3010, the value of log₁₀ 5 is: