Question

Is (ab)² equivalent to ab², why or why not?

Answer 1

(ab)² and ab² are not equal. When you have something in parentheses being squared, you have to square everything inside, so in the case of (ab)², you have to "distribute" the ² to both variables inside. That gives you a²b², not just ab².

If the abstract way is kind of confusing for you, just pick two random numbers for a and b and plug them in to test it. Say a = 3 and b = 4. Then

(3*4)² = 3*4²

(12)² =  3*16

144 ≠ 48