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Is the associative property of multiplication a regular associative problem but with factors?
There is only one associative property for multiplication: there is not a separate "regular" version.
What is the definition of assocative property of multiplication?
The associative property definition is this : you can group two numbers multiply them together then multiply that product by the other number. For example (3x3)x3=27 so basically all the associative property is about is grouping the numbers in different ways and making the problem faster and easier depending on what numbers you are multiplying. Hope that makes it easier 
What property is illustrated by this problem(5x6)x35x(6x3)?
If there is an equals sign between the 3 and 5 of 35, then it is the associative property of multiplication.
In the following problem what property allows you to multiply 5 by 2 before multiplying by 13?
I am guessing your problem is to compute 5 times 2 times 13. In this case, the property you are using the associative property.
Can associative property can be applied to the subtraction problem below when x equals 0 or 1?
I really can't say, because you're not letting me see the subtraction problem below.
