Chapter 4.pdf - CHAPTER 4 Exponents and Polynomials Source Elementary Intermediate Algebra Fourth Edition Prepared and Edited by Dr Mohamad Hammoudi

Chapter 4.pdf - CHAPTER 4 Exponents and Polynomials Source...

This preview shows page 1 - 13 out of 51 pages.

CHAPTER 4 Exponents and Polynomials Source: Elementary & Intermediate Algebra, Fourth Edition Prepared and Edited by: Dr. Mohamad Hammoudi
Image of page 1
Topics of Chapter 4 4.1: Positive Integer Exponents. 4.2: Zero and Negative Exponents and Scientific Notation. 4.3: Introduction to Polynomials. 4.4: Addition and Subtraction of Polynomials. 4.5: Multiplication of Polynomials and Special Products. 4.6: Division of Polynomials. 2
Image of page 2
4.1: Positive Integer Exponents Objectives: 4.1.1: Use exponential notation 4.1.2: Simplify expressions with positive integer exponents 3
Image of page 3
Exponents Instead of writing 2 . 2 . 2 . 2 . 2 . 2 . 2, we may write 2 7 Instead of writing a . a . a . a . a, we may write a 5 We call ( a ) the base on the expression and ( 5 ) the exponent , or power . a 5 is read as “ a to the fifth power.” Definition of Exponential Expression: An expression of this type is said to be in exponential form . 4
Image of page 4
4.1.1: Use Exponential Notation Examples: Write each of the following, using exponential notation. 1. 3 . 3 . 3 . 3 . 3 2. 5y . 5y . 5y 3. w . w . w . w 5
Image of page 5
Product Rule for Exponents Let’s consider what happens when we multiply two expressions in exponential form with the same base . Notice that the product is simply the base taken to the power that is the sum of the two original exponents. 6
Image of page 6
4.1.2: Simplify Expressions with Positive Integer Exponents Examples: Simplify each expression. 1. b 4 . b 6 2. (2a) 3 . (2a) 4 3. ( 2) 5 . ( 2) 2 4. (10 7 ) . (10 11 ) 7
Image of page 7
4.1.2: Simplify Expressions with Positive Integer Exponents Using the product rule for exponents together with the commutative and associative properties, simplify each expression. Multiply the coefficients and add the exponents by the product rule. Examples: Using the product rule for exponents together with the commutative and associative properties, simplify each expression. 1. (x 4 ) (x 2 ) (x 3 ) (x) 2. (3x 4 ) (5x 2 ) 3. (2x 5 y) (9x 3 y 4 ) 4. ( 3x 2 y 2 ) ( 2x 4 y 3 ) 8
Image of page 8
Quotient Rule for Exponents 9
Image of page 9
4.1.2: Simplify Expressions with Positive Integer Exponents Examples: Simplify each expression. 1. 2. 3. 4. 5. x x 4 10 a a 7 8 7w 63w 5 8 b 8a b 32a 2 5 4 10 10 6 16 10
Image of page 10
Product-Power Rule for Exponents (xy) 3 = (xy)(xy)(xy) = (x . x . x) . (y . y .y) = x 3 y 3 Examples: Simplify each expression. 1. (2x) 3 2. ( 4x) 4 11
Image of page 11
Power Rule for Exponents (3 2 ) 3 = (3 2 )(3 2 )(3 2 ) = (3)(3)(3)(3)(3)(3) = 3 6 Examples: Simplify each expression.
Image of page 12
Image of page 13

You've reached the end of your free preview.

Want to read all 51 pages?

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern

Stuck? We have tutors online 24/7 who can help you get unstuck.
A+ icon
Ask Expert Tutors You can ask You can ask You can ask (will expire )
Answers in as fast as 15 minutes