1 5 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.

Exponential Expressions Power Exponential Expression Exponent 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.

Exponential Expressions 5 5 squared = 25 5 5 cubed 5 5 5 = 125

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

Exponential Expressions

Inverse Operations Add – Subtract Multiply – Divide Powers – Roots

Square Roots Radical Principal Square Root Radicand What are the roots of 25? 5, – 5 or ± 5 What is ? 5

Square Roots 4 – 9 ± 8 Not a real number

Order of Operations PEMDAS Also roots Left to right!!! Parentheses = Grouping Symbols ( ) [ ] Grouping Symbols? ? ? No Yes

Undefined

1 1 3 4 4 1 3 1

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

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.

Simplify using order of operations. a) 18 b) 6 c) 30 d) 36 1. 5 Copyright © 2011 Pearson Education, Inc. Slide 1 - 19

Simplify using order of operations. a) 18 b) 6 c) 30 d) 36 1. 5 Copyright © 2011 Pearson Education, Inc. Slide 1 - 20

Simplify using order of operations. a) b) c) d) undefined 1. 5 Copyright © 2011 Pearson Education, Inc. Slide 1 - 21

Simplify using order of operations. a) b) c) d) undefined 1. 5 Copyright © 2011 Pearson Education, Inc. Slide 1 - 22