The associative property of multiplication states that the way in which factors are grouped in a multiplication problem does not change their product. In other words, \( (a \cdot b) \cdot c = a \cdot (b \cdot c) \).
Looking at the options provided:
A. \( (3 \cdot 5) \cdot 2 = (3 \cdot 5) \cdot 2 \) - This simply reiterates the same expression and does not demonstrate the associative property.
B. \( (3 \cdot 5) + 2 = (3 + 5) \cdot 2 \) - This is not demonstrating the associative property of multiplication; instead, it mixes addition and multiplication incorrectly.
C. \( (3 \cdot 5) \cdot 2 = 3 \cdot (5 \cdot 2) \) - This correctly demonstrates the associative property of multiplication because it shows that you can regroup the numbers in multiplication.
D. \( (3 + 5) \cdot 2 = 3 + (5 \cdot 2) \) - This demonstrates the distributive property, not the associative property.
Therefore, the correct answer is C. \( (3 \cdot 5) \cdot 2 = 3 \cdot (5 \cdot 2) \).