Section 1.2 Exponents & Radicals Objectives: To review exponent rules To review radicals To review rational exponents

Integer Exponents an = a · a · · · · · a The number a is called the base and n is called the exponent.

Ex 1. Simplify

Zero & Negative Exponents If a ≠ 0 is any real number and n is a positive integer, then a0 = 1 and a–n =

Ex 2. Simplify 1

Laws of Exponents Law Example 1) 2) 3) 4) 5)

Class Work Simplify 1. 2. 3. 4. 5.

Laws for Negative Exponents Law Example 6. 7.

Ex 3 Simplify a) b)

Class Work 6. 7.

Radicals The symbol √ means: “the positive square root of.” Thus,

nth Roots If 24 = 16, then it follows that . If n is any positive integer, then the principal nth root of a is defined as follows: If n is even, we must have a ≥ 0 and b ≥ 0.

Ex 4. Simplify a) b) c) d)

Properties of nth Roots Property Example 1. 2. 3.

Property Example 4. 5.

Ex 5. Simplify

Class Work 8. 9. 10.

Rational Exponents For example, and,

Ex 6. Simplify

Class Work 11. 12. 13. 14.