There are several number properties that GMAT test takers need to know / memorize.  A lot of these seem simple at first glance; however, the GMAT is very good at finding ways to make straightforward concepts difficult.  Additionally, there are number property concepts that are not as straightforward as others.  One of the more difficult concepts is exponent properties.

Remember: exponents simply count the number of times something is multiplied by itself.

With exponents, the most important concept to take into the test is the concept of similar bases.  If we have similar bases, the number properties of exponents allow us to manipulate them.  For instance, and do not allow us to manipulate them.  However, if the bases are the same, we can simplify the terms.

“Ok. I got the same base.  Now what?”

For the test, memorize the times that exponents need to be added, multiplied, or subtracted.  Flipping the way we look at exponents will help you memorize what to do when the time comes.

• Add Exponents: We add the exponents together when we are multiplying terms with exponents with each other.  For example: 
• Multiple Exponents: We multiply the exponents together when we have a term with an exponent raised to another exponent.  For example: 
• Subtract Exponents: We subtract exponents when we are dividing terms with exponents by each other.  For example: 

What about the following statement? .  What can we do with the terms when we are adding them together?  Nothing.  You have to work out each term and add the result.

Our last point is what to do with negative exponents.  Negative exponents can be simplified by dividing 1 by the term.  For example: is simply: .

Continue to work on your number properties questions.  These are the source of some frustrating questions.  However, a few simple principles will get you through it.