Simplify the given mathematical expression: $1+4 x^{-3}\left(-3 x^{2}+2\right)$

Step 1 ：Given the mathematical expression: \(1+4 x^{-3}(-3 x^{2}+2)\)

Step 2 ：Distribute the multiplication across the terms in the parentheses: \(1+4 x^{-3}(-3 x^{2}) + 4 x^{-3}(2)\)

Step 3 ：Simplify the expression: \(1 - 12x^{-1} + 8x^{-3}\)

Step 4 ：Final Answer: The simplified form of the given mathematical expression is \(\boxed{1 - \frac{12}{x} + \frac{8}{x^{3}}}\)