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

Answer

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Answer

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

Steps

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 $\boxed{1 - \frac{12}{x} + \frac{8}{x^{3}}}$