{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

lesson02

# lesson02 - THE UNIVERSITY OF AKRON Mathematics and Computer...

This preview shows pages 1–6. Sign up to view the full content.

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 I am 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 1995–2000 D. P. Story Last Revision Date: 2/2/2000

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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 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 = 0. (2) Needless to say, we define a 0 = 1, for all a = 0.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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 0 = 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 (that’s 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 students—I’m not saying you necessarily—have 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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 73

lesson02 - THE UNIVERSITY OF AKRON Mathematics and Computer...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online