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What Is an Exponent in Math? Your Guide

what is an exponent in math: x squared

Let’s get straight to your question: What is an exponent in math? Well, it’s the repeated multiplication of a specific number by itself. The number of times this value is multiplied by itself is indicated by the value of the exponent.

Let's define exponents and explore the basic rules of exponentiation, which is the process of raising one quantity to the power of another.

What Is an Exponent in Math?

Exponents are usually written in superscript, which is when a small number is placed above and to the right of the base:

what is an exponent in math: superscript

The base number x represents the value that is being multiplied by itself. The value of n is the exponent, which represents the number of times the base number will be multiplied by itself. In short, x will always be multiplied by itself n times.

Different Types of Exponents

Two of the most common exponents are 2 and 3. When exponent 2 is used, you are squaring the value of the base number or raising it to the second power. That means you’re multiplying the number by itself once. 6² = 6x6

With exponent 3, you are cubing the value of the base number or raising it to the third power. 3³ = 3 x 3 x 3.

Here are some examples of squaring and cubing:

what is an exponent in math: examples of squaring and cubing

Negative Exponents

The rules for negative exponents are different from those of positive exponents.

When you have a negative exponent, you have to put the x value in the denominator. The numerator is 1. The exponent becomes positive. It applies to the full fraction:

what is an exponent in math: negative exponent into fraction

It's essentially the same thing as raising a number to the power of a positive exponent, except that you have to divide this value by 1. Here's an example:

5 to the negative 3

The first thing you need to do with this negative exponentiation is inverse it. That means writing it as a fraction where the value of 5 is denominator and 1 is the numerator:

negative exponentiation

Next you will apply the exponent of 3, which can now be written as a positive exponent, to both parts of the fraction. You’ll divide to get the correct answer in decimal form (if it’s requested).

fraction to decimal

Using Exponents

Exponents indicate the number of times a given number is multiplied by itself. Though positive exponents are more common in math, learning to use negative exponents will help you move onto more complex rules of exponents such as product rules and power rules.

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