Paul's Online Math Notes
Algebra/Trig Review / Algebra / Exponents   
If you were affected by the server issues last night I apologize. Over the years the traffic on the site has increased significantly and it's reaching the point that my server is having issues handling the heavy traffic that comes at the end of the semester. Luckily I've got a new more powerful server setup almost ready to go that should be able to handle the increased traffic for the foreseeable future. It is currently scheduled to "go live" on Wednesday, May 11 2016 at 10:30 Central Standard Time. Unfortunately this is the earliest possible day to do the switch over between servers.

In the mean time the website is liable to be somewhat unreliable during the peak usage times at night and for that I apologize.

May 5, 2016

Algebra/Trig Review
  Next Chapter Trigonometry
Algebra (Introduction) Previous Section   Next Section Absolute Value
Exponents    [Show All Solutions]

Simplify each of the following as much as possible.



Show Solution

All of these problems make use of one or more of the following properties.



This particular problem only uses the first property.



Remember that the y’s in the last two terms can’t be combined!  You can only combine terms that are products or quotients.  Also, while this would be an acceptable and often preferable answer in a calculus class an algebra class would probably want you to get rid of the negative exponents as well.  In this case your answer would be.



The 2 will stay in the numerator of the first term because it doesn’t have a negative exponent.



Show Solution



Not much to this solution other than just adding the exponents.



Show Solution



Note that you could also have done the following (probably is easier….).



In the second case I first canceled an x before doing any simplification.


In both cases the 2 stays in the denominator.  Had I wanted the 2 to come up to the numerator with the x I would have used  in the denominator.  So watch parenthesis!



Show Solution

There are a couple of ways to proceed with this problem.  I’m going to first simplify the inside of the parenthesis a little.  At the same time I’m going to use the last property above to get rid of the minus sign on the whole thing.



Now bring the exponent in.  Remember that every term (including the 2) needs to get the exponent.



Recall that  so you can’t go any further with this.



Show Solution

Don’t make this one harder than it has to be.  Note that the whole thing is raised to the zero power so there is only one property that needs to be used here.




Algebra (Introduction) Previous Section   Next Section Absolute Value
  Next Chapter Trigonometry

Algebra/Trig Review / Algebra / Exponents   

© 2003 - 2016 Paul Dawkins