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1.7 Exponential Notation and the Order of Operations 1 Exponential Form A form of writing the product of a factor that repeats Base: The base is the factor being repeatedly multiplied Exponent: The exponent is a small number written to the right of the base and raised a half space. It indicates the number of bases being multiplied. Base Exponent (or power) How to say it. Exponent: 2 – squared or to the second power 3 – cubed or to the 3 rd power 4 – to the fourth power etc. Next Slide

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1.7 Exponential Notation and the Order of Operations 2 Example 1. a) Evaluate 3 4 b) Evaluate 5 2 Solutions: Your Turn Problem #1 a) Evaluate 5 3 b) Evaluate 7 2 Answers: a)125 b)49 Procedure: To evaluate a number in exponential form Step 1:Rewrite as repeated multiplication. Step 2:Multiply the repeated multiplications. A number with an exponent of 1 is simply equal to the number Exponents of One and Zero. A number with an exponent of 0 is equal to 1. It doesnt make too much sense right now. The explanation will come later once we have learned a few algebra tools. Your Turn Problem #2 a) Evaluate 4 0 b) Evaluate 12 1 Answers: a)1 b)12

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1.7 Exponential Notation and the Order of Operations 3 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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1.7 Exponential Notation and the Order of Operations 4 Step 1. Parentheses: None Step 2 Exponents: None Step 3. Multiplication or Division Step 4. Addition & Subtraction Answer: 19 Example 3. a) Simplify: b) Simplify: 4 + 3(12 –7) 4 + 3(5) Answer: 19 Answers: Your Turn Problem #3 Evaluate the following. Step 1. Parentheses Step 2 Exponents: None Step 3. Multiplication or Division Step 4. Addition & Subtraction 4 + (15)

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1.7 Exponential Notation and the Order of Operations 5 Step 1. Parentheses. No operations to perform in the parentheses. Step 2. Exponents. 8 – Step 3. Multiplication or Division: none. Step 4. Addition & Subtraction: left to right. Answers: Your Turn Problem #4 Evaluate the following. Answer: Step 1. Parentheses. Step 2. Exponents. Step 3. Multiplication or Division: left to right Answer: 54

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1.7 Exponential Notation and the Order of Operations 6 1 st perform the operations within the parentheses. 2 nd, perform the operations within the brackets. Your Turn Problem #5 Evaluate the following. Answer: 19 Answer: 22 Answers: The End B.R

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