Mastering Exponents: Rules and Examples

1. Chapter 1 Basic Concepts

2. Chapter Sections 1.1 – Study Skills for Success in Mathematics, and Using a Calculator 1.2 – Sets and Other Basic Concepts 1.3 – Properties of and Operations with Real Numbers 1.4 – Order of Operations 1.5 – Exponents 1.6 – Scientific Notation

3. Exponents § 1.5

4. exponent 34 base 4 factors of 3 Exponents In the expression 34, the 3 is called the base, and the 4 is called the exponent. 34 is read “3 to the fourth power” and means 3·3·3·3 = 34 = 81 Note that x + x + x + x = 4x and x · x · x · x = x4

5. -x2 vs. (-x)2 An exponent refers only to the number or letter that directly precedes it unless parentheses are used to indicate otherwise. –x2 = –(x)(x) (–x)2 = (–x)(–x) = x2 Example: –52 = –(5)(5) = –25 (–5)2 = (–5)(–5) = 25

6. Product Rule for Exponents Example: Multiply each expression. a.) b.) c.)

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

8. Zero Exponent Rule a0 = 1, x  0 Example: Simplify each expression. a.) b.) c.)

9. Negative Exponent Rule . Example: Write each expression without negative exponents. a.) b.) c.)

10. Power Rule for Exponents Example: Simplify each expression. a.) b.) c.)

11. Raising a Product to a Power Example: Simplify each expression. a.) b.)

12. Raising a Quotient to a Power Example: Simplify each expression. a.)