CMA Foundation · Fundamentals of Business Mathematics and Statistics · 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. Each factor gives a power of (difference)(sum), which is a difference of squares, and the three differences p²-q², q²-r² and r²-p² add up to zero, so the result is a^0 = 1.
- Aa^(p+q+r)
- Ba
- Ca^0 = 1Correct
- Da^(pq+qr+rp)
Explanation
Sum the exponents: (p-q)(p+q) + (q-r)(q+r) + (r-p)(r+p) = (p²-q²) + (q²-r²) + (r²-p²) = 0. So the expression is a^0 = 1. Options with non-zero powers come from adding the exponents without expanding the differences of squares.
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