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**Objective A: To Evaluate Exponential Expressions**

Repeated multiplication can be expressed in exponential form: When an algebraic expression (problem) is written in exponential form with a base that is a number, it can be multiplied out from its factored form. This is called to “evaluate the expression”. Example 1. a) Evaluate 64 When more than two bases in an expression are to be evaluated, write each separately in factored form, then find the products of all factors. b) Evaluate 23 52 Solutions: Your Turn Problem #1 a) Evaluate 53 b) Evaluate 72 42 Answers: 125 784 To use a calculator to evaluate an exponential expression: Type 5 then the exponent button. The exponent button may either be xy or . Then type in 3. You should see 125 on your calculator.

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Solutions: If the base is negative, the base must be written (with its negative sign) inside a set of parentheses. If a negative appears without parentheses, then the base is positive but after evaluating, find the opposite. If the base is negative and it is raised to an even exponent, the answer will be positive. If the base is negative and it is raised to an odd exponent, the answer will be negative. Your Turn Problem #2 Evaluate the following. Answers:

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**Order of Operations Agreement**

Multiplication and division come before addition and subtraction unless placed within parenthesis. Then there are exponents. When are they to be simplified? To keep it all straight, it is imperative that you memorize the following-- the complete Order of Operations Agreement. Please note the first letter of each step. Procedure: For Order of Operation Step 1: Parentheses: perform operations inside parentheses or other grouping symbols Step 2: Exponents: simplify (evaluate) exponential notation expressions Step 3: Multiply or divide as they appear from left to right Step 4: Add or subtract as they appear from left to right It is advisable to use a mnemonic device ) a memory trick) to help you memorize. A commonly used acronym is PEMDAS (Parenthesis, Exponents, Multiply, Divide, Add and Subtract), or Please Excuse My Dear Aunt Sally. From now on in algebra, when you are asked to “simplify” remember to use the Order of Operations Agreement (PEMDAS). In simplifying, work vertical; for each step recopy the entire problem. For each line of the problem, perform only the step being performed in the Order of Operations. Please note, in most problems, where you are to simplify, not all operations appear. Perform the operations, that do appear in order, but skip the operations that do not appear

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**Example 3. a) Simplify: –13 + 2 3**

b) Simplify: 4 – 3(12 –15) Step 1. Parentheses: None Step 2 Exponents: None Step 3. Multiplication or Division –13 + 6 Step 4. Addition & Subtraction Answer: –7 Step 1. Parentheses Step 2 Exponents: None Step 3. Multiplication or Division 4 – 3(–3) 4 – (–9) Step 4. Addition & Subtraction Answer: 13 4 + 9 4 – 3(–3) Note: The subtraction can be changed to addition, then change the sign of the number after the subtraction symbol. 4 +(–3)(–3) 4 + 9 Your Turn Problem #3 Evaluate the following. Answers:

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**Step 1. Parentheses. No operations to perform in the parentheses.**

Step 2. Exponents. –8 – Answer: –14 –23 + 9 Step 3. Multiplication or Division: none. Step 4. Addition & Subtraction: left to right. Step 1. Parentheses. Step 2. Exponents. Step 3. Multiplication or Division: left to right Answer: 54 Your Turn Problem #4 Evaluate the following. Answers:

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**1st perform the operations within the parentheses**

1st perform the operations within the parentheses. 2nd, perform the operations within the brackets. Answer: 1 1st perform the operations within the parentheses. 2nd, perform the operations within the brackets. Answer: 102 -4(-2)=+8 Your Turn Problem #5 Evaluate the following. Answers:

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**1st simplify the numerator and denominator.**

It may be easier for some to write out the numerator and simplify it, then simplify the denominator. Then write the numerator over the denominator, then simplify if possible. Answer: –2 Your Turn Problem #6 Answer: The End B.R.

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Chapter 1 Section 3 Copyright © 2011 Pearson Education, Inc.

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