Exponents

What Is an Exponent?

An exponent tells you how many times a number (or other quantity) is multiplied by itself.

Dictionary Definition

The Oxford English Dictionary defines an exponent as "a symbol denoting the number of times a particular quantity is to be taken as a factor to produce the power indicated."

Understanding Exponents

It is easier to understand exponents with an example.

Imagine we wanted to multiply 3 by itself 2 times. We would write 3 with a small 2 written to the right and above it: 32.

3 squared equals 3 times 3. 2 is the exponent.

Powers, Bases and Exponents

3 squared
  • A power is the product of multiplying a number by itself. 32 is equal to 3 multiplied by itself 2 times, which equals 9.

  • 3 is called the base. It is the number that is multiplying itself.

  • 2 is called the exponent. It tells you how many times the base is multiplying itself.

Real Examples of an Exponent

Some real examples of exponents are given below.

  • The power below has an exponent of 3:

    4 to the power of 3
  • The power below has an exponent of 4:

    2 to the power of 4
  • The exponent can also be a letter. The power below has an exponent of n:

    2 to the n

Negative Exponents

Exponents can also be a negative number.

A negative exponent tells you how many times to divide 1 by the number. For example, 3−2 means divide 1 by 3, 2 times:

3 to the minus 2 equals 1 divided by 3 squared

A negative exponent means put the base under 1 (or turn it upside-down if the base is a fraction), and make the exponent positive.

Read more about how to find a negative exponent

Fractional Exponents

An exponent can be a fraction.

A fractional exponent means finding a root of a number.

For example, 3½ means the square root of 3:

3 to the half equals the square root of 3

See Also

What is a power? What is a base? The laws of exponents