To solve for \( v \) in the equation \( (100 \cdot 33) \cdot 39 = 100 \cdot (v \cdot 39) \), we can use the associative property of multiplication.
According to the associative property, the way we group the factors in multiplication does not change the product. Therefore, we can rewrite the left-hand side as follows:
\[ (100 \cdot 33) \cdot 39 = 100 \cdot (33 \cdot 39) \]
Now, we set the two sides of the equation equal to each other:
\[ 100 \cdot (33 \cdot 39) = 100 \cdot (v \cdot 39) \]
Now, since both sides of the equation have \( 100 \) as a factor, we can divide both sides by \( 100 \) (as long as \( 100 \neq 0 \)). This gives us:
\[ 33 \cdot 39 = v \cdot 39 \]
Now, we can divide both sides by \( 39 \) (assuming \( 39 \neq 0 \)):
\[ 33 = v \]
Thus, the value of \( v \) is:
\[ \boxed{33} \]
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