1. Exponents, Roots, and Order of Operations
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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.
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2. 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.

3. Exponential Expressions5
= 25
5 squared 5
5 cubed
= 125

4. 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!!!

5. Exponential Expressions

6. Inverse Operations
Add – Subtract
Multiply – Divide
Powers – Roots

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

8. Square Roots 4
– 9
± 8
Not a real number

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

14. Undefined

16. 1 3 4 1 4 1 3 1

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

18. 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.

19. Simplify using order of operations.
b) 6
c) 30
d) 36
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20. Simplify using order of operations.
b) 6
c) 30
d) 36
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21. Simplify using order of operations.b) c)
d) undefined
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22. Simplify using order of operations.b) c)
d) undefined
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