Consider the data on $x$ taking the values $0,2,4,8$, $\ldots, 2^n$ with frequencies ${ }^n C_0,{ }^n C_1,{ }^n C_2, \ldots,{ }^n C_n$ respectively. If the mean of this data is $\frac{728}{2^n}$, then n is equal to $\_\_\_\_$ .
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