2. CHAPTER 10 Exponents and Polynomials Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 10.1Integers as Exponents 10.2Working with Exponents 10.3Scientific Notation 10.4Addition and Subtraction of Polynomials 10.5Introduction to Multiplying and Factoring Polynomials

3. OBJECTIVES 10.1 Integers as Exponents Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. aEvaluate algebraic expressions containing whole- number exponents. bExpress exponential expressions involving negative exponents as equivalent expressions containing positive exponents.

4. 10.1 Integers as Exponents a Evaluate algebraic expressions containing whole-number exponents. Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

5. 10.1 Integers as Exponents THE EXPONENTS 1 AND 0 Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

6. EXAMPLE 10.1 Integers as Exponents a Evaluate algebraic expressions containing whole-number exponents. 1 Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

7. EXAMPLE 10.1 Integers as Exponents a Evaluate algebraic expressions containing whole-number exponents. 4 Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

8. 10.1 Integers as Exponents b Express exponential expressions involving negative exponents as equivalent expressions containing positive exponents. Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The pattern used to help define the exponents 1 and 0 can also be used to define negative-integer exponents:

9. 10.1 Integers as Exponents NEGATIVE EXPONENTS Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. For any nonzero numbers a and b, and any integer n, (A base raised to a negative exponent is equal to the reciprocal of the base raised to a positive exponent.)

10. EXAMPLE 10.1 Integers as Exponents b Express exponential expressions involving negative exponents as equivalent expressions containing positive exponents. Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Write an equivalent expression using positive exponents. Then simplify.

11. EXAMPLE 10.1 Integers as Exponents b Express exponential expressions involving negative exponents as equivalent expressions containing positive exponents. Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

12. 10.1 Integers as Exponents b Express exponential expressions involving negative exponents as equivalent expressions containing positive exponents. Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

13. 10.1 Integers as Exponents b Express exponential expressions involving negative exponents as equivalent expressions containing positive exponents. Slide 13Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Our work indicates that to divide by a base raised to a negative power, we can instead multiply by the opposite power of the same base. This will shorten our work.

14. EXAMPLE 10.1 Integers as Exponents b Express exponential expressions involving negative exponents as equivalent expressions containing positive exponents. Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Write an equivalent expression using positive exponents.