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MathNet 2017-part-06 — 176 problems (EN–VI) Question 66

Math Olympiad Vault · MathNet 2017-part-06 — 176 problems (EN–VI)

Question 66

Let $n$ be a natural number. Which of the expressions listed below is equivalent to the expression
$$\frac{\sqrt[n]{n^{n}} \cdot \sqrt[n+n]{n^{n}}}{\sqrt[n]{n^{n+n}}}$$?

(A) 1
(B) $\sqrt[n]{n}$
(C) $n$
(D) $\sqrt{n}$
(E) $n^{-\frac{1}{2}}$