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Algebra - Integer Exponents
We will start off this chapter by looking at integer exponents. In fact, we will initially assume that the exponents are positive as well. We will look at zero and negative exponents in a bit. We should also use this opportunity to remind ourselves about parenthesis and conventions that we have in regard to exponentiation and parenthesis. This will be particularly important when dealing with negative numbers.
Consider the following two cases. These will have different values once we evaluate them. When performing exponentiation remember that it is only the quantity that is division properties exponents homework help to the left of the exponent that gets the power.
In the first case there is a parenthesis immediately to the left so that means that everything in the parenthesis gets the power. So, division properties exponents homework help, in this case we get. In the second case however, the 2 is immediately to the left of the exponent and so it is only the 2 that gets the power.
The minus sign will stay out in front and will NOT get the power. In this case we have the following. We put in some extra parenthesis to help illustrate this case. The point of this discussion is to make division properties exponents homework help that you pay attention to parenthesis. Be careful. Also, this warning about parenthesis is not just intended for exponents. We will need to be careful with parenthesis throughout this course.
In the case of zero exponents we have. Here is a quick example of this property. We have the following definition for negative exponents, division properties exponents homework help. Here are a couple of quick examples for this definition. Here are some of the main properties of integer exponents.
Accompanying each property will be a quick example to illustrate its use. We will be looking at more complicated examples after the properties. Notice that there are two possible forms for the third property.
Which form you use is usually dependent upon the form you want the answer to be in. For example, property 4 can be extended as follows. We only used four factors here, but hopefully you get the point.
Property 4 and most of the other properties can be extended out to meet the number of factors that we have in a given problem.
There are several common mistakes that students make with these properties the first time they see them. Contrast this with the following case. Again, note the importance of parenthesis and how they can change an answer!
Once again, notice this common mistake comes down to being careful with parenthesis. This will be a constant refrain throughout these notes. We must always be careful with parenthesis. Misusing them can lead to incorrect answers. There are many different paths that we can take to get to the final answer for each of these. In the end the answer will be the same regardless of the path that you used to get the answer.
All that this means for you is that as long as you used the properties you can take the path that you find the easiest. The path that others find to be the easiest may not be the path that you find to be the easiest. That is okay, division properties exponents homework help. That is one of the more common mistakes that students make with these simplification problems. At this point we need to evaluate the first term and eliminate the negative exponent on the second term.
We further simplified our answer by combining everything up into a single fraction. This should always be done. The middle step in this part is usually skipped. All the definition of negative exponents tells us to do is move the term to the denominator and drop the minus sign in the exponent. So, from this point on, that is what we will do without writing in the middle step.
In this case we will first use property 10 on both terms and then we will combine the terms using property 1. Finally, we will eliminate the negative exponents using the definition of negative exponents. There are a couple of things to be careful with in this problem. Second, in the final step, the stays in the numerator since there is no negative exponent on it. We will use the definition of negative exponents to move all terms with negative exponents in them to the denominator.
Also, property 8 simply says that if there is a term with a negative exponent in the denominator then we will just move it to the numerator and drop the minus sign. Now simplify. Do not get excited if all the terms move up to the numerator or if all the terms move down to the denominator. That will happen on occasion. This example is similar to the previous one except there is division properties exponents homework help little more going on with this one.
The first step will be to again, get rid of the negative exponents as division properties exponents homework help did in the previous example. Notice this time, division properties exponents homework help, unlike the previous part, there is a term with a set of parenthesis in the denominator, division properties exponents homework help.
Because of the parenthesis that whole term, including the 3, will move to the numerator. There are several first steps that we can take with this one. After we do that we will use property 5 to deal with the exponent that is on the parenthesis.
When we have exponents of 1 we will drop them, division properties exponents homework help. This one is very similar to the previous division properties exponents homework help. The main difference is negative on the outer exponent. Now at this point we can use property 6 division properties exponents homework help deal with the exponent on the parenthesis. Doing this gives us. Before leaving this section we need to talk briefly about the requirement of positive only exponents in the above set of examples.
This was done only so there would be a consistent final answer. In many cases negative exponents are okay and in some cases they are required. In fact, if you are on a track that will take you into calculus there are a fair number of problems in a calculus class in which negative exponents are the preferred, if not required, form.
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Example 1 Simplify each of the following and write the answers with only positive exponents. For this one we will use property 10 first. Here is the work for this part.
Chapter 7 Lesson 2 Division Properties of Exponents Homework Answers
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Jun 01, · In this section we will start looking at exponents. We will give the basic properties of exponents and illustrate some of the common mistakes students make in working with exponents. Examples in this section we will be restricted to integer exponents. Rational exponents will be discussed in the next section Get Answers to All Your Math Homework Questions: From Algebra, Calculus, Stats or Trigonometry, we’ve got you covered. We have a math expert for online homework help, studying and test prep on all topics and blogger.com offer math homework help which trains students first to understand the mathematical problems and then find the most efficient way to Nov 14, · The Yup Homework Help app provides homework help for math, chemistry, and physics anytime and anywhere. You can connect with expert tutors 24/7 for academic support. The service does have a subscription fee but you can sign up for a
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