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 2 5 Exponent

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. 5 2 2 2 2 2 2 32 Exponential Expressions 5 squared 2 5 5 = 25

5 5 cubed 3 5 5 5 5 = 125 Exponential Expressions Base 2 3 2

9 2 3 2 9 2 3 2 9 3 2 3

8 3 2 3 8 2 3 8 3 Opposite of Parentheses are important!! 3 3

2 No difference Exponent Evaluate 2 2 3 Watch for negative numbers raised to an EVEN power!!! Exponential Expressions 3 3 27 3 3 3

125 5 5 5 5 Inverse Operations Add Subtract Multiply Divide Powers Roots Square Roots

Radical Principal Square Root 25 5 Radicand What are the roots of 25? 5, 5 or 5 What is 25 ? 5 Square Roots 16 4 81

9 64 8 25 Not a real number Order of Operations PEMDAS Also roots Left to right!!! Parentheses = Grouping Symbols ( ) [ ]

Grouping Symbols??? 2 3 No 2 3 4 Yes 5 3 4 5 3 4 5 7 15 4 35 19 4

3 2 5 2 4 6 7 5 16 5 8 24 35 16 40 16 40 24 11 3 12 64 4 2 2 12 64 4 2 8 12 16 16

12 16 16 12 100 64 18 3 2 36 18 3 2 6 18 3 2 6 6 2 6 12 18 7 2 5 2 6 3 14 2 7 3 2 6 3 12

7 3 36 3 12 7 3 36 36 4 0 Undefined 2 3 5 6 2 1 49 2 3 5 6 3 49 2 3 5 3 49

9 5 3 7 9 15 7 17 3 2 9 16 4 4 3 81 27 9 1 9 16 4 12 81 27 9 1 3 12 9

16 4 27 9 1 4 4 3 13 12 3 2 9 8 1 12 12 12 4 3 1

3 1 3 1 9 1 12 9 12 3 4 1 4 4 1 16 9 16 4 4 27 4 27 9

3 1 3 1 4 3 16 13 4 3 12 12 12 Arithmetic Mean or Average To find the arithmetic mean, or average, of n numbers, divide the sum of the numbers by n. Arithmetic mean = x1 x2 ... xn n 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. 546 92 96 81 89 95 93 6 6 91 Simplify using order of operations. 6 2 18 9 6 a) 18 b) 6 c) 30 d) 36 1.5

Copyright 2011 Pearson Education, Inc. Slide 1- 19 Simplify using order of operations. 6 2 18 9 6 a) 18 b) 6 c) 30 d) 36 1.5 Copyright 2011 Pearson Education, Inc. Slide 1- 20

Simplify using order of operations. 2 4 23 a) 8 300 b) 250 361 c) 2 11 6 30 2 4 2 d) undefined

1.5 Copyright 2011 Pearson Education, Inc. Slide 1- 21 Simplify using order of operations. 2 4 23 a) 8 300 b) 250 361 c) 2 11

6 30 2 4 2 d) undefined 1.5 Copyright 2011 Pearson Education, Inc. Slide 1- 22