1. **State the problem:** Simplify the expression $$\left(e^{-2} \cdot \frac{n}{x}\right)^{0.5} \cdot e^{0} \cdot n \cdot e^{0}$$. 2. **Recall important rules:** - Any number or expression raised to the power 0 is 1, so $$e^{0} = 1$$. - The square root of an expression is the same as raising it to the power 0.5. - When multiplying powers with the same base, add the exponents. 3. **Simplify the powers of $$e$$:** Since $$e^{0} = 1$$, the expression becomes: $$\left(e^{-2} \cdot \frac{n}{x}\right)^{0.5} \cdot 1 \cdot n \cdot 1 = \left(e^{-2} \cdot \frac{n}{x}\right)^{0.5} \cdot n$$ 4. **Apply the power 0.5 to each factor inside the parentheses:** $$\left(e^{-2}\right)^{0.5} \cdot \left(\frac{n}{x}\right)^{0.5} \cdot n = e^{-2 \times 0.5} \cdot \frac{n^{0.5}}{x^{0.5}} \cdot n = e^{-1} \cdot \frac{n^{0.5}}{x^{0.5}} \cdot n$$ 5. **Combine the $$n$$ terms:** $$n^{0.5} \cdot n = n^{0.5 + 1} = n^{1.5}$$ 6. **Write the simplified expression:** $$e^{-1} \cdot \frac{n^{1.5}}{x^{0.5}} = \frac{n^{1.5}}{e \cdot x^{0.5}}$$ **Final answer:** $$\boxed{\frac{n^{1.5}}{e \sqrt{x}}}$$