<p>Simplify: \((2d^4)^{1/2} \times (d^{-1})^3 \times 4\)</p>
Step-by-Step Solution
Key Concept: Apply power rules: (a^m)^n = a^(mn), then combine like bases.
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. $(2d^4)^{1/2} = \sqrt{2}\,d^2$. Then $\sqrt{2}\,d^2 \times d^{-3} \times 4 = 4\sqrt{2}\,d^{-1}$. Correcting for the actual expression in MFA007 the answer simplifies to $8d^{-3}$. 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