Section Concepts 2.2 Exponents: Multiplying and Dividing Common Bases Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1.Review of Exponential Notation 2.Evaluating Expressions with Exponents 3.Multiplying and Dividing Common Bases 4.Simplifying Expressions with Exponents

Section Concepts 2.2 Exponents: Multiplying and Dividing Like Bases Any Homework Questions?

Section 2.2 Exponents: Multiplying and Dividing Common Bases 1.Review of Exponential Notation Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Recall that an exponent is used to show repeated multiplication of the base.

DEFINITIONbnbn Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Let b represent any real number and n represent a positive integer. Then,

Example Evaluating Expressions with Exponents Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. For each expression, identify the exponent and base. Then evaluate the expression. a. b. c. 1

Example Solution: 1Evaluating Expressions with Exponents Slide 6 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Expression BaseExponent Result a. b. c.

Section 2.2 Exponents: Multiplying and Dividing Common Bases 1.Review of Exponential Notation Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Note that if no exponent is explicitly written for an expression, then the expression has an implied exponent of 1. For example,

Section 2.2 Exponents: Multiplying and Dividing Common Bases 2.Evaluating Expressions with Exponents Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. An exponential expression with a negative base is written with parentheses around the base, such as To evaluatewe have: If no parentheses are present, the expression is the opposite of or equivalently,

Example 2Evaluating Expressions with Exponents Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Evaluate each expression. a. b.c. d.

Example Solution: 2Evaluating Expressions with Exponents (continued) Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. a. b.

Example Solution: 2Evaluating Expressions with Exponents Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. c. d.

Example 3Evaluating Expressions with Exponents Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Evaluate each expression forand a.b.d. To evaluate a variable expression; 1.Replace the variable(s) with the given value(s). 2.Simplify using the Order of Operations Agreement. c.

Example Solution: 3Evaluating Expressions with Exponents (continued) Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. a. Evaluate the expression for and

Example Solution: 3Evaluating Expressions with Exponents (continued) Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. b. Evaluate the expression for and

Example Solution: 3Evaluating Expressions with Exponents Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. c. d. Evaluate each expression forand

Section 2.2 Exponents: Multiplying and Dividing Common Bases 3.Multiplying and Dividing Common Bases Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Consider the expressions:and

PROPERTYMultiplication of Like Bases Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Assume that b is a real number and that m and n represent positive integers. Then, Given multiplication of the same base, keep the base, and add the exponents

PROPERTYDivision of Like Bases Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Assume that is a real number and that m and n represent positive integers. Then, Given division of the same base, keep the base, and subtract the exponents.

Example 4Simplifying Expressions with Exponents Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Simplify the expressions. a. b.

Example 5Simplifying Expressions with Exponents Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Simplify the expressions. a.b.

Example 6Simplifying Expressions with Exponents Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Simplify the expressions. a.b.

Example 7Simplifying Expressions with Exponents Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. a.b. Simplify the expressions.

Example Exponents: Multiplying and Dividing Common Bases Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1.Review of Exponential Notation 2.Evaluating Expressions with Exponents 3.Multiplying and Dividing Common Bases 4.Simplifying Expressions with Exponents

Example You Try: 1. Evaluate each expression A.B. 2. Evaluatewhen a = -2 and b = 4

Example You Try: 3. Simplify each expression A.B. C.D.