1. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Evaluate expressions involving exponents. Simplify expressions involving exponents. 2.2 Properties of Exponents

2. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Glossary Terms base exponent power 2.2 Properties of Exponents

3. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Definition of Integer Exponents Let a be a real number. If n is a natural number, then: a n = a  a  a ...  a, n times. If a is nonzero, then: a 0 = 1. If a is a natural number, then: 2.2 Properties of Exponents a –n = 1 anan.

4. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Properties of Exponents 2.2 Properties of Exponents Quotient of Powers amam anan = a m – n Product of Powers (a) m (a) n = a m + n Power of a Power (a m ) n = a mn Power of a Product (ab) n = a n b n Power of a Quotient a b n anan bnbn = Let a and b be nonzero real numbers. Let m and n be integers.

5. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Definition of Rational Exponents For all positive real numbers a: If n is a nonzero integers, then 2.2 Properties of Exponents If m and n are integers and n  0, then a 1 n = aa n. a m n = a 1 n m = aa n m.

6. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Simplify and evaluate expressions by using the Properties of Exponents. Key Skills 2.2 Properties of Exponents a. (3 2 ) 3 3434 = 3 (2)(3)  1 3434 = 3 6  3 –4 = 3 6 – 4 = 3 2 = 9 Use Power of a Power Property Definition of Integer Exponents Use the Product of Powers Property Simplify

7. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Simplify and evaluate expressions by using the Properties of Exponents. Key Skills 2.2 Properties of Exponents Use Power of a Quotient Property Use Power of a Power Property Simplify x3(y2)3x3(y2)3 z3z3 = x 3  y (2)(3) z3z3 = x3y6x3y6 z3z3 = xy 2 z 3 b. TOC