When a person doesn't know how to say a * a (aka a²), or is typing on keyboard and cannot bother to find the ² symbol, then he or she just says/types the power of.
the first case:umm...two and two...urh....two and a * and another two...uhm...TWO TO THE POWER OF TWO!
the second case:what is 4 to the power of 2?
4²? Oh sixteen...