Squares, square roots, and powers

The square of any number x is the product of the number times itself, denoted x². The term originates from the fact that the area of a square (with equal sides) is the length of a side times itself. The square of any nonzero number is positive, since the product of two negative numbers is positive, and the square of zero is zero. Conversely, any positive number must be the square of two numbers, x and −x. These are its square roots.

More generally, multiplying a number x by itself n times gives x to the power of n, written xn. Powers have their own combination rules, which arise from their meaning:

xn × xm = xn⁺m, (xn)m = xnm, x⁰ = 1, x¹ = x, and x⁻¹ = 1/X

It also follows from the formula (xn)m = xnm that the square root of a number can be thought of as that number raised to the power of one-half. 

                                      Example: