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**Exponents and Polynomials**

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**Chapter Sections 4.1 – Exponents 4.2 – Negative Exponents**

4.3 – Scientific Notation 4.4 – Addition and Subtraction of Polynomials 4.5 – Multiplication of Polynomials 4.6 – Division of Polynomials Chapter 1 Outline

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Exponents

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**Product Rule for Exponents**

When multiplying expressions with the same base, we keep the base and add the exponents. Example: Multiply each expression. a.)32 · 3 = 33 = b.) 24 · 22 = 26 = 64 c.) x · x4 = x5 d.) x3 · x6 = x9 e.) y4 · y7 = y11

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**Quotient Rule for Exponents**

Example: Divide each expression. a.) b.)

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**Zero Exponent Rule x0 = 1, x 0 Example: Simplify each expression.**

b.) x0 = 1 c.) (3x)0 = 1

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**Power Rule for Exponents**

(xm)n = xmn Example: Simplify each expression. a.) (x3)5 = x15 b.) (34)2 = 38 c.) (y5)7 = y35

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**Power of a Product Rule (xy) n = xnyn Example:**

Simplify the expression. a.) (a2b3) 4 = a8b12

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**Power of a Quotient Rule**

Example: Simplify each expression. a.) b.)

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**Expanded Power Rule for Exponents**

Example: Simplify the following expression. .

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1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-1 Polynomials and Polynomial Functions Chapter 5.

1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-1 Polynomials and Polynomial Functions Chapter 5.

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