1. The problem asks to simplify or expand the expression $n!^{1/n}$. 2. First, recall that $n!$ (n factorial) is the product of all positive integers from 1 to $n$: $$n! = 1 \times 2 \times 3 \times \cdots \times n.$$ 3. The expression $n!^{1/n}$ means we are taking the $n$th root of $n!$, which is $ (n!)^{\frac{1}{n}} $. 4. While this cannot be expanded into a simple closed form, we can express it using Stirling's approximation for better understanding: $$n! \approx \sqrt{2\pi n} \left(\frac{n}{e}\right)^n.$$ 5. Applying the $n$th root to both sides: $$ (n!)^{1/n} \approx \left( \sqrt{2\pi n} \left( \frac{n}{e} \right)^n \right)^{1/n} = (2\pi n)^{1/(2n)} \times \frac{n}{e}.$$ 6. As $n$ becomes large, $(2\pi n)^{1/(2n)}$ approaches $1$. 7. Therefore, for large $n$, $$ (n!)^{1/n} \approx \frac{n}{e}.$$ 8. So the expression $n!^{1/n}$ grows approximately like $n/e$ for large $n$. Final answer: The exact simplified form is just $n!^{1/n}$, but approximately we have $$n!^{1/n} \approx \frac{n}{e}$$ for large $n$.