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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Indices and Logarithms

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

The value is 1. Each bracket gives an exponent of the form (difference)(sum), namely a²-b², b²-c² and c²-a². These add up to zero, so the whole expression equals x^0, which is 1.

  1. Ax^(a+b+c)
  2. Bx^0 = 1Correct
  3. Cx^(2abc)
  4. Dx^(a²+b²+c²)

Explanation

The exponents are (a-b)(a+b) = a²-b², (b-c)(b+c) = b²-c², and (c-a)(c+a) = c²-a². Their sum is 0, so the expression equals x^0 = 1. Option x^(a²+b²+c²) arises from adding squares without the negative signs.

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