Evaluating (1.001)^3531

Q.1 If (1.001)1259 = 3.52 and (1.001)2062 = 7.85, then (1.001)3321 = (A) 2.23 (B) 4.33 (C) 11.37 (D) 27.64

Q.1 If (1.001)1259 = 3.52 and (1.001)2062 = 7.85, then (1.001)3321 =

(A) 2.23
(B) 4.33
(C) 11.37
(D) 27.64

Evaluating (1.001)3531 Using Exponential Laws

Problems involving exponential expressions with the same base are common in
competitive exams. Instead of direct calculation, such questions test the
application of the laws of indices. This solution explains how to
evaluate (1.001)3531 using the given values.

Concept Used

Law of exponents:

am+n = am × an

Step-by-Step Solution

Step 1: Split the Exponent

3531 = 1259 + 2062

Step 2: Apply the Exponent Rule

(1.001)3531 =
(1.001)1259 ×
(1.001)2062

Step 3: Substitute Given Values

= 3.52 × 7.85

Step 4: Calculate

3.52 × 7.85 = 27.632 ≈ 27.64

Option-wise Explanation

(A) 2.23 ❌
Too small; likely obtained by incorrect division of powers.

(B) 4.33 ❌
Close to a given value, but ignores exponent addition.

(C) 11.37 ❌
Results from partial or incorrect multiplication.

(D) 27.64 ✅
Correctly applies am+n = am × an.

Final Answer

(1.001)3531 = 27.64

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