1. Exponents and Polynomials

2. 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

3. Exponents

4. 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

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

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

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

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

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

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