What is the HCF of 3^{29}-9 and 3^{38}-9?
- A. 3^{9}-1
- B. 3^{11}-1
- C. 3^{11}-3
- D. 3^{11}-9 ✓
Correct Answer: D. 3^{11}-9
Explanation
Rewrite the expressions as 9(3^{27}-1) and 9(3^{36}-1). Using the rule \text{HCF}(a^m-1, a^n-1) = a^{\text{HCF}(m,n)}-1, the HCF of the terms inside the parentheses is 3^{\text{HCF}(27,36)}-1 = 3^9-1. Multiplying the common factor 9 (or 3^2) back in: 3^2(3^9-1) = 3^{11}-9.
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