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

Simplify (5^(n+2) − 5^n) ÷ (5^(n+1) − 5^(n-1)).

The value is 5. Factor the numerator as 5^n times 24 and the denominator as 5^(n-1) times 24. The 24s cancel, leaving 5^n divided by 5^(n-1), which equals 5.

  1. A5Correct
  2. B25/24
  3. C25
  4. D24/5

Explanation

Numerator: 5^n(25 − 1) = 24·5^n. Denominator: 5^(n-1)(25 − 1) = 24·5^(n-1). Ratio = 5^n/5^(n-1) = 5. Option 24/5 comes from factoring incorrectly.

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