To simplify the expression \( \frac{3}{49v^6} \), we can break it down as follows:
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The fraction can be rewritten by separating the constants and the variable components: \[ \frac{3}{49} \cdot \frac{1}{v^6} \]
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The constant part \( \frac{3}{49} \) is already in its simplest form since 3 and 49 have no common factors.
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The part with the variable \( \frac{1}{v^6} \) is already simplified as well.
Thus, the simplified form of the expression is: \[ \frac{3}{49v^6} \]
Since \( v > 0 \), the expression remains valid without any further restrictions.
So, the final answer is: \[ \frac{3}{49v^6} \]