# Exponents, Roots, and Order of Operations

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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.

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.

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

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!!!

Exponential Expressions

Inverse Operations Add – Subtract Multiply – Divide Powers – Roots

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

Square Roots 4 – 9 ± 8 Not a real number

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

Undefined

1 3 4 1 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.
b) 6 c) 30 d) 36 Copyright © 2011 Pearson Education, Inc. 1.5

Simplify using order of operations.
b) 6 c) 30 d) 36 Copyright © 2011 Pearson Education, Inc. 1.5

Simplify using order of operations.
b) c) d) undefined Copyright © 2011 Pearson Education, Inc. 1.5

Simplify using order of operations.
b) c) d) undefined Copyright © 2011 Pearson Education, Inc. 1.5

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