<p>If \(\left(\sqrt{2}\right)^{-1/32} \cdot 2^{1/32} = \left(\dfrac{1}{\sqrt{2}}\right)^n\), then \(n =\) (refer MFA009 for exact expression)</p>
Step-by-Step Solution
Key Concept: Convert everything to base 2 and equate exponents.
Notice that the best first move is to reveal the hidden structure in the expression. A clever move here is to rewrite the problem in the form where the standard theorem or identity applies cleanly. Express both sides as powers of 2 and equate exponents. The equation reduces to a linear equation in $n$, giving $n = 4$. Now, we invoke the power of that idea, simplify patiently, and then check that the final answer really fits the original problem.
Correct Answer: B