How does the power of a power property of exponents differ from the product of powers property?

My teacher said it was something we should think about when doing the homework. The elimination method is the method where you add the equal equations (in slope-intercept form) to each other.

Would it just be the addition property of equality?

With the congruence properties of triangles, what is the differene between the angle-angle-side property and the angle-side-angle property?

If something just says “communiative property” ? What does that refer to? And are there several types of communative properties?