Exponentiation: Basic Definitions

Exponentiation

Basic Conceptions and Definitions

Basic Definitions

Radicals

Exponentiation: Basic Definitions

In the expression an,

a is called the base,

n is the exponent (or index) of power, and

an is the nth power of a (or a raised to the nth power).

For example, the exponents of the quantities

x3, 42, 5z and 3n

are, respectively,

3, 2, z and n.

By definition, a number raised to the power of zero is 1:

a0= 1.

The first power of a quantity is the quantity itself:

a1 = a.

If a quantity is raised to the second power then the quantity is said to be squared:

4 squared is 42= 4·4.

Likewise, "a cubed" means that the index of power is 3:

5 cubed is 53= 5·5·5.

The number a–1 is called the reciprocal of a. By definition,

A number with a negative index of power is the reciprocal of the number with the positive index: