Exponents and Polynomials

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

Exponents

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 = 127 b.) 24 · 22 = 26 = 64 c.) x · x4 = x5 d.) x3 · x6 = x9 e.) y4 · y7 = y11

Quotient Rule for Exponents Example: Divide each expression. a.) b.)

Zero Exponent Rule x0 = 1, x  0 Example: Simplify each expression. b.) x0 = 1 c.) (3x)0 = 1

Power Rule for Exponents (xm)n = xmn Example: Simplify each expression. a.) (x3)5 = x15 b.) (34)2 = 38 c.) (y5)7 = y35

Power of a Product Rule (xy) n = xnyn Example: Simplify the expression. a.) (a2b3) 4 = a8b12

Power of a Quotient Rule Example: Simplify each expression. a.) b.)

Expanded Power Rule for Exponents Example: Simplify the following expression. .