Question

which uses associative property for equivalent expression of (I * sqrt7) * 5

Answer 1

Use the associative property of multiplication: (a·b)·c = a·(b·c).

Apply it to (I * sqrt7) * 5:
(I * sqrt7) * 5 = I * (sqrt7 * 5) = I * (5 sqrt7) = 5 * I * sqrt7.

So an equivalent (and simplified) expression is 5 I sqrt7 (often written 5√7·I).