What is an Exponent?

MATH REVIEW: USEFUL MATH FOR EVERYONE

SECTION 3. WHAT IS AN EXPONENT?

An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 2³) means:

2 x 2 x 2 = 8.

2³ is not the same as 2 x 3 = 6.

Remember that a number raised to the power of 1 is itself. For example,

a¹ = a

5¹ = 5.

There are some special cases:

1. a⁰ = 1

When an exponent is zero, as in 6⁰, the expression is always equal to 1.

a⁰ = 1

6⁰ = 1

14,356⁰ = 1

2. a^-m = 1 / a^m

When an exponent is a negative number, the result is always a fraction. Fractions consist of a numerator over a denominator. In this instance, the numerator is always 1. To find the denominator, pretend that the negative exponent is positive, and raise the number to that power, like this:

a^-m = 1 / a^m

6^-3 = 1 / 6³

You can have a variable to a given power, such as a³, which would mean a x a x a. You can also have a number to a variable power, such as 2^m, which would mean 2 multiplied by itself m times. We will deal with that in a little while.

to Exponents, Page 2

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