# Understanding the Negative Exponent Rule

Before you learn to understand and apply the **Negative Exponent Rule**, let’s recap what you already know about positive exponents.

For example, 5^2, or 5 squared, is equal to 5x5, or 25.

**But what would change if the exponent (2 in this case) was negative instead of positive?**

In math, when you think of the word *negative* or *negate*, the implication is that you must perform the **opposite or inverse operation**.

With positive exponents, you perform multiplication.

So, **with negative exponents, you perform the opposite or inverse of multiplication**, which is…

**Division **(because division is the inverse operation of multiplication).

Now you are ready to use the Negative Exponent Rule

**Negative Exponent Rule in 3 Easy Steps**

Now let’s look at the previous example again, except this time the exponent is -2 (negative two).

**Step One: Rewrite the Value with Negative Exponent as a Fraction**

Since we are performing division (the inverse of multiplication), we will **rewrite the value as a fraction with a numerator of one**.

**Step Two: Trash the Negative Sign and Move the Value to the Denominator**

To complete the fraction, get rid of the negative sign in front of the exponent and move the remaining value (5 squared) to the denominator of the fraction.

Notice that 5 to the negative second power is equal to one over 5 to the positive second power.

**Step Three: Trash the Negative Sign and Move the Value to the Denominator**

The final step is to simplify rewriting 5 squared as 25 and concluding that 5^-2 is equal to 1/25 or 0.04.

Looking for a visual representation of how the negative exponent rule works?

**Check out the free video lesson below to learn more about how the negative exponent rule.**

**Free Negative Exponents Worksheet**

This lesson includes a free Negative Exponent Rule worksheet that accompanies the video lesson. Click the link below to get yours!

Download your free Negative Exponents Worksheet Lesson Guide PDF

**Share your ideas, questions, and comments below!**

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**By Anthony Persico**

*Anthony is the content crafter and head educator for YouTube's** MashUp Math** . You can often find me happily developing animated math lessons to share on my **YouTube channel** . Or spending way too much time at the gym or playing on my phone.*