A Proven Guide to Subtracting Exponents

Are you frustrated with subtracting exponents?  Are your exponent worksheets making you crazy?  If you want to completely understand the laws of exponents you have come to the right place.

All the math help you need is right here on one website.  In this section we explain the exponent rules clearly and at your pace.  We recommend that you take a look at our video demos in this section to see how easy we make it to grasp the laws of exponents.

If you prefer to read along for a while first, we will go through the two things that can be meant by exponent subtraction.

Subtracting Exponents: When do we do it?

The only time we will actually subtract exponents is when two identical bases are dividing each other.  Let’s use a numerical example to start.  We know thatmath.  We also know that math andmath.  Therefore we can rewrite the equation  math asmath.  In short, we see thatmath.

Notice that if we just focus on the exponents 5, 3, and 2, thatmath.  We can do this to the exponents because the bases are the same in both the top and the bottom of the fraction.

We can do the same thing if all of the terms are algebraic.  For example,mathis the same kind of question as above except we have used letters in the bases instead of numbers.  If we want to look at an example that is even more challenging we can consider the following: math.  Notice how we only subtracted the exponents from the same base.  Themathfrom themathand the mathfrom the math.

Subtracting Exponents two terms

This is a completely different topic from what was discussed in the above paragraphs.  In this case, we are not talking about division at all.  When we have to subtract algebraic terms from each other, the coefficients can be different but the letters and their exponents must be identical.

Here is what we mean, math because the exponent on the ‘a’ is 3 in both terms and the exponent on the ‘b’ is 5.  The coefficient in the first term is 1 and is 3 in the second term.  Since the algebraic term math is the same for both, we can simply do the subtractionmath to get the value for the new coefficient.

If we are given the examplemath, we may wonder what happened to wind up with two terms in the answer instead of only one.  Let’s look at the exponents on themathand math.  We notice that the exponent on the y in mathis 5 whereas the exponent on the y in the other two terms is 6.  This means that we cannot add or subtract the mathto the other terms in the equation.  This is why the math is seen on both the left and right sides of the equation.

Moving Forward

The subtracting exponents page is just one of several public pages dealing with the laws of exponents.  Some of the other exponent rules can be found on the following pages below;

What we recommend most however, is to click on our video demonstration pages and watch our interactive videos on the related topics.  Once you are armed with the information that we deliver in those videos, you will have received the math help you truly needed to succeed on your next set of exponent worksheets. 

Contact Us

If you have any questions, comments, or topic requests, please email us.  We will respond to your emails promptly.  We hope to contribute to your ongoing math success.

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