Find the minimum value of
\[\frac{x^7 + 32x^2 + 128}{x^3}\]for $x > 0.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the minimum value of
\[\frac{x^7 + 32x^2 + 128}{x^3}\]for $x > 0.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
48
Find the minimum value of
\[\frac{x^7 + 32x^2 + 128}{x^3}\]for $x > 0.$
train