<p>The expansion \(a^m\left\{\left(1 + \dfrac{b}{a}\right)^m\right\}\) is valid only when:</p>
Step-by-Step Solution
Key Concept: The binomial expansion (1 + x)^n is valid only when |x| < 1, so for (1 + b/a)^m we need |b/a| < 1, which means |b| < |a|.
<p><strong>Step 1:</strong> The binomial expansion (1 + x)^n is valid when |x| < 1 for real or fractional exponents.</p><p><strong>Step 2:</strong> In the given expression a^m{(1 + b/a)^m}, we identify x = b/a.</p><p><strong>Step 3:</strong> For the expansion to be valid, we need |b/a| < 1.</p><p><strong>Step 4:</strong> This simplifies to |b| < |a|.</p><p>∴ Answer: C (The expansion is valid when |b| < |a|)</p>
Correct Answer: C