Exponentiation - Background and Terminology

Background and Terminology

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, 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".

Exponentiation may be generalized from integer exponents to more general types of numbers.

When this article refers to 'an odd power' of a number it means the exponent is an odd number, not that the result is odd. For instance 23 which is 8 is an odd power of 2 because the exponent is 3. This is the usual usage and applies to any similar form like an even power, negative power, or positive power.