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About this Lesson
 Type: Video Tutorial
 Length: 1:37
 Media: Video/mp4
 Use: Watch Online & Download
 Access Period: Unrestricted
 Download: MP4 (iPod compatible)
 Size: 17 MB
 Posted: 06/26/2009
This lesson is part of the following series:
College Algebra: Full Course (258 lessons, $198.00)
College Algebra: Basics & Prerequisites (37 lessons, $52.47)
College Algebra: Exponents (4 lessons, $4.95)
Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, College Algebra. This course and others are available from Thinkwell, Inc. The full course can be found athttp://www.thinkwell.com/student/product/collegealgebra. The full course covers equations and inequalities, relations and functions, polynomial and rational functions, exponential and logarithmic functions, systems of equations, conic sections and a variety of other AP algebra, advanced algebra and Algebra II topics.
Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.
He has also taught at UTAustin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".
Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, padic analysis, the geometry of numbers, and the theory of continued fractions.
Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.
About this Author
 Thinkwell
 2174 lessons
 Joined:
11/14/2008
Founded in 1997, Thinkwell has succeeded in creating "nextgeneration" textbooks that help students learn and teachers teach. Capitalizing on the power of new technology, Thinkwell products prepare students more effectively for their coursework than any printed textbook can. Thinkwell has assembled a group of talented industry professionals who have shaped the company into the leading provider of technologybased textbooks. For more information about Thinkwell, please visit www.thinkwell.com or visit Thinkwell's Video Lesson Store at http://thinkwell.mindbites.com/.
Thinkwell lessons feature a starstudded cast of outstanding university professors: Edward Burger (PreAlgebra through...
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Okay, now one of the things that we have to become very intimate with and very intimate with fast, are exponents. Now I now what you are saying. You're saying, gee, you know exponents, who needs them? Well, let me just tell you that in fact exponents are so important and will make your life so much more happy if you embrace them instead of repelling them. Let me show you why.
Suppose for example you just want to like you know write down something like x x x x. Do you know how much ink you would waste if you want to write that all out? And it's so boring, it's so repetitious x and x and x that people are going to say, Gee they're going to put me to sleep; this is boring. Whereas you know of course with exponents you can just abbreviate that and say x to the fifth power. This is great. Do you see the power of this? Let me show you another example. Suppose I said to you, solve this equation, 5 x x x  2 x x = 0. First of all that looks so long you say Oh my god it's impossible there are so many x's in there. How would I even attack that thing? Hard.
However, if you write it in the fancy exponent way, it would be 5x^3  2x^2 = 0. And then with a little bit of factoring magic, we can solve this thing in no time at all. So, the power of using exponents is that it allows us to take things that would of otherwise be sort of awkward just to hold on to and to make them short, concise, and great. So, what we are going to do next is, that's right folks, we are going to start exercising our exponents. See you in the gym.
Prerequisites
Exponents
An Introduction to Exponents Page [1 of 1]
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