What is the value of $(2x^3) \div (2x)^3$ when $x = 2007$? Express your answer as a common fraction.
<|im_start|>system
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<|im_start|>user
What is the value of $(2x^3) \div (2x)^3$ when $x = 2007$? Express your answer as a common fraction.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac14
What is the value of $(2x^3) \div (2x)^3$ when $x = 2007$? Express your answer as a common fraction.
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