1. Start with the expression: $$2x^{-1/2}$$. 2. Recall that $$x^{-1/2} = \frac{1}{x^{1/2}} = \frac{1}{\sqrt{x}}$$, so the expression is $$2 \times \frac{1}{\sqrt{x}} = \frac{2}{\sqrt{x}}$$. 3. Note that the user's equation $$2x^{-1/2} = 2 \times \frac{1}{x^{2}}$$ is incorrect because $$x^{-1/2}$$ is not equal to $$\frac{1}{x^{2}}$$. 4. Therefore, the correct simplified form is $$\frac{2}{\sqrt{x}}$$. 5. Next, evaluate $$\sqrt[3]{4^{1-5}}$$. 6. Simplify the exponent inside the root: $$1 - 5 = -4$$, so the expression is $$\sqrt[3]{4^{-4}}$$. 7. Rewrite the cube root as a power: $$\left(4^{-4}\right)^{1/3} = 4^{-4/3}$$. 8. Express in index notation: $$4^{-\frac{4}{3}}$$, meaning the reciprocal of $$4^{4/3}$$. Final answers: - $$2x^{-1/2} = \frac{2}{\sqrt{x}}$$. - $$\sqrt[3]{4^{1-5}} = 4^{-\frac{4}{3}}$$.