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**Exponents, Roots, and Order of Operations**

1.5 Exponents, Roots, and Order of Operations 1. Evaluate numbers in exponential form. 2. Evaluate square roots. 3. Use the order-of-operations agreement to simplify numerical expressions. 4. Find the mean of a set of data. Copyright © 2011 Pearson Education, Inc.

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**Exponential Expressions**

Power Exponential Expression Base Base: The number that is repeatedly multiplied. Exponent: A symbol written to the upper right of a base number that indicates how many times to use the base as a factor. Evaluate: Find the value.

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**Exponential Expressions**

5 = 25 5 squared 5 5 cubed = 125

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**Watch for negative numbers raised to an EVEN power!!!**

Exponential Expressions Base Exponent Evaluate Opposite of Parentheses are important!! No difference Watch for negative numbers raised to an EVEN power!!!

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**Exponential Expressions**

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Inverse Operations Add – Subtract Multiply – Divide Powers – Roots

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**Square Roots Radical Principal Square Root Radicand**

What are the roots of 25? What is ? 5, – 5 or ±5 5

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Square Roots 4 – 9 ± 8 Not a real number

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**PEMDAS Order of Operations Left to right!!! ( ) [ ] Also roots**

Parentheses = Grouping Symbols Grouping Symbols??? No ( ) [ ] Yes

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Undefined

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1 3 4 1 4 1 3 1

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**Arithmetic Mean or Average**

To find the arithmetic mean, or average, of n numbers, divide the sum of the numbers by n. Arithmetic mean =

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**Arithmetic Mean or Average**

Bruce has the following test scores in his biology class: 92, 96, 81, 89, 95, 93. Find the average of his test scores.

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**Simplify using order of operations.**

b) 6 c) 30 d) 36 Copyright © 2011 Pearson Education, Inc. 1.5

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**Simplify using order of operations.**

b) 6 c) 30 d) 36 Copyright © 2011 Pearson Education, Inc. 1.5

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**Simplify using order of operations.**

b) c) d) undefined Copyright © 2011 Pearson Education, Inc. 1.5

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**Simplify using order of operations.**

b) c) d) undefined Copyright © 2011 Pearson Education, Inc. 1.5

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