The expression b2 = b·b is called the square of b because the area of a square with side-length b is b2.
The expression b3 = b·b·b is called the cube of b, because the volume of a cube with side-length b is b3.
So 32 is pronounced "three squared", and 23 is "two cubed".
The exponent says how many copies of the base are multiplied together. For example, 35 = 3·3·3·3·3 = 243. The base 3 appears 5 times in the repeated multiplication, because the exponent is 5. Here, 3 is the base, 5 is the exponent, and 243 is the power or, more specifically, the fifth power of 3, 3 raised to the fifth power, or 3 to the power of 5.
The word "raised" is usually omitted, and very often "power" as well, so 35 is typically pronounced "three to the fifth" or "three to the five".
