Exponents, Roots, and Order of Operations

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

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