The Trick to Simplifying Expressions with Exponents

Exponents. While designed to make expressions easier to read and understand, they often cause more confusion for kids. To make matters worse, when they first learn about exponents, teachers don’t expect kids to actually solve expressions with exponents, they just expect them to simplify them. While kids learn all about adding exponents with common bases, multiplying exponents, or arranging them in order from highest to lowest, the trick to simplifying expressions with exponents (at least at the beginning) may be breaking them down into their busiest form.

What is an Exponent?

what is an exponent

In short, an exponent means a number or an expression is multiplied by itself. For example, 4³ just means 4x4x4. So when given an expression with exponents and asked to simplify it, one of the easiest ways to do it is to break down the exponents into their busiest form or what they literally mean.

So 4³ (4²)  could be written as 4x4x4x4x4. From there, it’s easy to add all of the fours together, realize there are 5 of them, and learn that  4³ (4²) can be simplified to read .

The same method works when simplifying expressions with exponents involving division.

The expression above can be rewritten to read:

To simplify the expression, all someone has to do is cross out the number of 5s each level has in common. So the equation becomes:

Since 5º equals 1 and any number divided by one equals itself, the equation can be even further simplified to 5².

Understanding Exponents

Kids can complete the Solving Exponents Worksheet from Math Game Time to help them better understand exponents and the concept of simplifying expressions with exponents. Once kids start to understand what an exponent is and how to simplify equations with exponents, they can begin to play more complex games and complete more advanced worksheets that involve these pesky little numbers.

Otter Rush has kids solve very simple equations with exponents as they race through the water. For example, kids may see x²=4 and must select 2 as the correct answer or they may see  and must select 3 as the correct answer.

Learning to break down answers can help kids solve these problems quickly. For example, with the expression x²=4 kids will quickly think “okay, what number multiplied by itself twice equals 4?” and with  kids will think “how many times do I have to multiply 3 to get 27?”

Of course to get kids to think this way, they must have solid multiplication skills, Math Game Time’s multiplication games can help kids build their multiplication skills so they’re ready to tackle simplifying exponents.


Leave a Reply

Your email address will not be published. Required fields are marked *


You may use these HTML tags and attributes: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <strike> <strong>