Powers
Copyright Scott Storla 2015
An Introduction to Powers
Copyright Scott Storla 2015
Procedure – Order of Operations
Begin with the innermost grouping idea and work out;
Explicit grouping ( ), [ ], { }
Implicit grouping
Operations in the numerator or denominators of fractions.
Operations in radicands, exponents or logarithmic arguments.
1. Start to the left and work right simplifying each operation beyond the basic
four as you come to them.
2. Start again to the left and work right simplifying each multiplication or
division as you come to them.
3. Simplify all terms.
4. Start again to the left and work right simplifying each addition or
subtraction as you come to them.
Copyright Scott Storla 2015
Operations and Operators
Operation
Addition
Operator(s)
+

Subtraction
Multiplication
 
 

Division
2
Power
Root
Absolute value
Logarithm
Exponential
log ln
10
Copyright Scott Storla 2015
e
Base
exponent
3
 Power
2  3 3
9
The second power of three.
Three to the second power.
On a calculator the exponent key
often looks like ^ or x y or y x or x .
Copyright Scott Storla 2015
Simplify
02  0
12  1
22  4
32  9
42  16
52  25
62  36
72  49
82  64
92  81
102  100
Copyright Scott Storla 2015
Simplify
03  0
33  27
13  1
43  64
23  8
53  125
( 1)3  1
( 2)3  8
( 4)3  64
( 5)3  125
Copyright Scott Storla 2015
( 3)3  27
Are these the same or different?
If they’re the same, what is the value?
If they’re different, what are the values?
22  2  2  4
2  1 2  2  1 4  4
2
( 2)  ( 2)( 2)  4
2
Copyright Scott Storla 2015
Fill in the blanks using the words term, factor,
sum, product, difference, quotient, base,
exponent and power.
3
2
Given 5(6  4 )
5 is a _____, 6  42 is a _____, (6  42 ) is a
3
2
2
_____, 4 is a_____, 3 is an_____, (6  4 ) is a_____ and a
_____and the entire expression is a_____.
Copyright Scott Storla 2015
Fill in the blanks using the words term, factor,
sum, product, difference, quotient, base,
exponent and power.
Given (42  52 ) 1  2 
3
42 is both a_____ and a_____, 42  52
is a_____, (42  52 ) is a_____, 1  2 is a _____, (1  2)3 is a_____
and a_____ and the entire expression is a _____.
Copyright Scott Storla 2015
Fill in the blanks using the words term, factor,
sum, product, difference, quotient, base,
exponent and power.
Given
62  52
 4  3 2
2 is an_____, 5 is a_____, (4  3)2 is a _____,
62  52 is a_____ and the entire expression is a_____.
Copyright Scott Storla 2015
An Introduction to Powers
Copyright Scott Storla 2015
Powers and the Order of Operations
Copyright Scott Storla 2015
Count the number of operators, discuss the
order and then simplify the expression.
33  32  3
27  9  3
18  3
21
Copyright Scott Storla 2015
Count the number of operators, discuss the
order and then simplify the expression.
2
3
10  8  2
100  8  8
800  8
100
Copyright Scott Storla 2015
Count the number of operators, discuss the
order and then simplify the expression.
 7   4  2  3 
2
49  4  2  3 
49  24
25
Copyright Scott Storla 2015
Count the number of operators, discuss the order and
then simplify the expression.
 6  3   (62  32 )
2
 9 2  (36  9)
 9 2  (45)
81  45
36
Copyright Scott Storla 2015
Count the number of operators, discuss the
order and then simplify the expression.
 1
2
 5  2  9 
1  5  2  9 
1  ( 90)
91
Copyright Scott Storla 2015
Count the number of operators, discuss the order and
then simplify the expression.
22  42
2  4
2
4  16
 2 
2
12
4
3
Copyright Scott Storla 2015
Count the number of operators, discuss the
order and then simplify the expression.
64  64
1 64  64
1 1,296  1,296
1,296  1,296
2,592
Copyright Scott Storla 2015
Count the number of operators, discuss the order and
then simplify the expression.
(5  2)2   6  4 2 


2
2
(3)   2 


9  4
2
2
[5] 2
25
Copyright Scott Storla 2015
2
Powers and the Order of Operations
Copyright Scott Storla 2015
Powers and the Order of Operations
Grouping
Copyright Scott Storla 2015
Procedure – Order of Operations
Beginning with the innermost grouping idea and working out;
Explicit Grouping ( ), [ ], { }
Implicit Grouping
Operations in the numerators and
denominators of fractions
Operations in Radicands
Operations in Exponents
1. Start to the left and work right simplifying each operation beyond the basic four
as you come to them.
2. Start again to the left and work right simplifying each multiplication or division as
you come to them.
3. Start again to the left and work right simplifying each addition or subtraction as
you come to them.
Copyright Scott Storla 2015
Count the number of operators, discuss the order and
then simplify the expression.


4 1
6


1 4  

 3  3



4
6


 1 4  
 6

 64 


  6 3 


3
3
1,296 
 216 


63
216
3
Copyright Scott Storla 2015
3
Count the number of operators, discuss the order and
then simplify the expression.
 7  12 
2 1
 10  6 
 5 2 1   4 23
 5 3   4 5
125  1,024
1,149
Copyright Scott Storla 2015
23
Simplify
32 1  24 3
 1 1
5
33  21
 1 1
5
27  2
 1 1
5
25
 1 1
5
5  1 1
4 1
5
Copyright Scott Storla 2015
Powers and the Order of Operations
Grouping
Copyright Scott Storla 2015
Powers
Copyright Scott Storla 2015