To expand \( (X - \frac{1}{2}X)^5 \), we first simplify the expression inside the parentheses:
\[ X - \frac{1}{2}X = \frac{2}{2}X - \frac{1}{2}X = \frac{1}{2}X \]
So we need to expand:
\[ \left(\frac{1}{2}X\right)^5 \]
Using the property of exponents, we can expand this as follows:
\[ \left(\frac{1}{2}\right)^5 \cdot X^5 \]
Calculating \(\left(\frac{1}{2}\right)^5\):
\[ \left(\frac{1}{2}\right)^5 = \frac{1}{2^5} = \frac{1}{32} \]
Thus, we have:
\[ \left(\frac{1}{2}X\right)^5 = \frac{1}{32} X^5 \]
Therefore, the expanded form of \( (X - \frac{1}{2}X)^5 \) is:
\[ \frac{1}{32} X^5 \]
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