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Unformatted text preview: ~ w mptii menu THE UNIVERSITY OF AKRON Mathematics and Computer Science Lesson 2: Exponents & Radicals Directory Table of Contents Begin Lesson 2 A n A l g e b r a R e v i e w Iam DP S N Z Q R C a 3 a 4 = a 7 ( ab ) 10 = a 10 b 10 ( ab (3 ab 4)) = 2 ab 4 ( ab ) 3 ( a 1 + b 1 ) = ( ab ) 2 ( a + b ) ( a b ) 3 = a 3 3 a 2 b + 3 ab 2 b 3 2 x 2 3 x 2 = (2 x + 1)( x 2) 1 2 x + 13 = 0 = x = 26 G = { ( x, y )  y = f ( x ) } f ( x ) = mx + b y = sin x i n T e n L e s s o n s Copyright c 19952000 D. P. Story Last Revision Date: 2/2/2000 Lesson 2: Exponents & Radicals Table of Contents 2. Exponents and Radicals 2.1. Integer Exponents 2.2. The Law of Exponents How to Multiply or Divide Two Powers How to Calcu luate a Power of a Product or Quotient How to Compute a Power of a Power 2.3. Radicals Properties of Radicals 2.4. Fractional Exponents 2. Exponents & Radicals This lesson is devoted to a review of exponents, radicals, and the infamous Laws of Exponents. The student must have the skills to manipulate exponents without error . 2.1. Integer Exponents Let a be a number, and n N be a natural number . The symbol a n is defined as a n = a a a a a  {z } n factors (1) That is, a n is the product of a with itself n times. Sometimes, negative exponents enter into the mix. These are defined by a n = 1 a n where n N and a 6 = 0. (2) Needless to say, we define a = 1, for all a 6 = 0. Section 2: Exponents & Radicals Thus, the symbol a k is defined for all integers k Z : for positive integers as in equation (1) , 2 3 = (2)(2)(2) = 8; for negative integers as in equation (2) , 2 3 = 1 / 2 3 = 1 / 8; and for zero, 2 = 1. Terminology. The symbol a k is called a power of a . We say that a k has a base of a and that k is the exponent of the power of a . Numerical calculations offer no challenge to the student (thats you). The more interesting case is when there are symbolic quantities in volved; however, there is one situation involving numerics (and sym bolics) in which some studentsIm not saying you necessarilyhave a weakness. Consider the following . . . Quiz. Suppose you wanted to square the number 3, what would be the correct notational way of writing that? (a) 3 2 (b) ( 3) 2 (c) (a) and (b) are equivalent To effectively manipulate expressions involving symbolics, we must be the masters of the Laws of Exponents to be taken up shortly; just now, however, I want to illustrate how the definitions of a k are applied. Section 2: Exponents & Radicals Illustration 1. Here are several important illustrations of the tech niques revolving about the definitions given in equations (1) and (2) ....
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This note was uploaded on 09/24/2009 for the course CHEM 333 taught by Professor Baird during the Spring '09 term at UC Davis.
 Spring '09
 Baird

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