Question 382642
(I had to look this up because I wasn't familiar with the name)

Seems like the principle of powers says that if a = b, then a^n = b^n (however we must be careful when we take square, cubed, etc. roots, as I'll show later).

For example, we can solve {{{sqrt(x+2) = 7}}} by squaring both sides to obtain {{{x+2 = 49}}} --> x = 47.

However, suppose we were given the equation {{{x^4 = 1}}}. Taking the fourth root of both sides it is easy to establish x = 1. It is correct, but there are three other values of x that satisfy: -1, i, and -i. These roots are often called "roots of unity."