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

Integer Exponents a n = 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 a 0 = 1 and a –n =

Ex 2. Simplify 1

Laws of Exponents LawExample 1) 2) 3) 4) 5)

Class Work Simplify

Laws for Negative Exponents LawExample 6. 7.

Ex 3 Simplify a)b)

Class Work 6. 7.

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

n th Roots If 2 4 = 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 n th Roots PropertyExample

PropertyExample 4. 5.

Ex 5. Simplify

Class Work

Rational Exponents For example, and, For example,

Ex 6. Simplify

Class Work

HW #2 p21 1-7odd, 9,12,15,17,23-43odd, 45-65eoo, eoo – every other odd