Ex. 15x3/5x = 3x2
To divide these two monomials, first divide the coefficients just like usual. 15/5 = 3. For the exponents with the same base, you subtract the exponents when dividing so 3 (from x3) minus 1 (from x1) equals 2 so your variable is x2. This gives you an answer of 3x2.
Ex. 24a3c6/16a4c3 = 3c3/2a
First divide the coefficients, they both divide by 8 and so we are left with 3 on the top and 2 on the bottom. There is an a3 on the top which cancels out with the a4 on the bottom but we are still left with one a on the bottom. There is a c6 on the top which cancels out the c3 on the bottom and we are left with c3 on the top. This gives us our final answer of 3c3/2a.
Video:
http://www.youtube.com/watch?v=Mn4WuvIGUgI
Negative Exponents: More examples on page 210 of our textbook
x2/x5 = x2-5 =x-3
If we follow our exponent rules and subtract the exponents when we divide then the answer we get is x-3
x2/x5 = (x)(x)/(x)(x)(x)(x)(x) = 1/x3
This is the same problem but solved slightly differently and with a different answer. From this we can assume that
x-3 is equal to 1/x3
From this we can see that if you bring a negative exponent from the denominator to the numerator, and vice versa, that it then becomes a positive exponent.
Ex.
3a2x-2/axy-1 = 3a2y/ax3 = 3ay/x3
By bringing the bases with negative exponents from the numerator to the denominator, or from the denominator to the numerator we are left with all positive exponents. We moved the x-2 from the numerator to the denominator so it became
x2
and we brought the y-1 from the denominator to the numerator making it just y. From here all we needed to do was cancel the a's and we got 3ay/x3 as our answer.
Video:
http://www.youtube.com/watch?v=c4aiYf3fzVQ
Tips:
- When Dividing subtract exponents
- When Multiplying add exponents
- When raising a monomial to a power multiply exponents
- When raising monomial don't forget to raise the coefficient
Overall this post was outstanding and highlighted key points on what the whole concept of Dividing Monomials and Negative Exponents is all about. What particularly stood out to me was the two both acceptable ways of presenting or dividing a negative exponent. That's particularly important so we can understand that there's two great ways of showing it and not just one. But yes this blog was clear and complete and would help a lot with the understanding of this method. Good Job Sebastian!
ReplyDeleteThis was a very informative and well organized post. The format was very easy to follow, and there was a nice variety of practice problems that you explained. I Liked how whenever you explained a problem you said where it can be found in the book. Also the videos were a good addition to build off of what you were describing. Nice job Sebastian!!
ReplyDeleteThis was a very informative and well organized post. The format was very easy to follow, and there was a nice variety of practice problems that you explained. I Liked how whenever you explained a problem you said where it can be found in the book. Also the videos were a good addition to build off of what you were describing. Nice job Sebastian!!
ReplyDeleteSebastian, this post covers some nice exponent examples. I like how you did each example and then followed it up with a written description. I also liked that you explained why the negative exponent rule is true! The videos were nice additions (although, honestly, the first guy was a bit painful to watch, don't you think?) My only suggestion would be to use something like Notability to show your steps so readers can more easily see what is on the top and bottom of the fractions you were simplifying. Overall, nicely done!
ReplyDeleteThis was a very thorough blog! The format was very organized and easy to follow. It was very helpful how you gave an example, and then followed it with a description. The videos were also very informative, and the tips at the end were good reminders and helpful tips. Very nice job!
ReplyDelete