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CA Foundation · Quantitative Aptitude · Ratio and Proportion, Indices and Logarithms

The simplified value of (x^(a+b))^(a−b) × (x^(b+c))^(b−c) × (x^(c+a))^(c−a) is:

The value is 1. Each term simplifies to a difference of squares in the index: x^(a²−b²), x^(b²−c²) and x^(c²−a²). Their indices add up to zero, so the product is x^0, which equals 1.

  1. Ax^(a²+b²+c²)
  2. Bx^(2(a²+b²+c²))
  3. C1Correct
  4. Dx^(abc)

Explanation

Multiply powers within each term: x^(a²−b²) × x^(b²−c²) × x^(c²−a²). Adding the indices gives a²−b²+b²−c²+c²−a² = 0. So the result is x^0 = 1. Option x^(a²+b²+c²) comes from wrongly adding squares without the signs.

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