Question

Name the property the equation illustrates (ab)3=a(b3)

Answer 1

The answer to this rests on knowing that there are four properties of multiplication (which your teacher will likely expect you to know...):

These are:
1. commutative
2. associative
3. multiplicative identity
4. distributive

I won't define each of these -- they should be in your notes or textbook. Look them up.

In this case, we are multiplying three terms together -- on the left hand side the parentheses mean to multiply a and b first, then multiply that by 3. On the right hand side, we multiply b times 3 first, and then multiply the product by a.

This would be an example of the associative property of multiplication: when three or more factors are multiplied together, the product is the same regardless of how the factors are grouped.

Hope this helps!

Good luck