Date ___________________ 1D
Exponents
Name ___________________________________
Algebra I - Pd ____
Exponent
/
Base -->
34 = 81
<--Power
Read as "three to the fourth power" or "three raised to the fourth power"
The base is the number that is used as a factor in the product (what we multiply by itself)
The exponent tells us how many times the base is to be used as a factor (tells us how
many times to multiply the base by itself)
The power is a product of equal factors
n3 = n  n  n
n1 = n
n0 = 1
n-6 = 1
53 = 5  5  5 = 125
51 = 5
anything raised to the 1st power equals itself
0
5 =1
anything raised to the 0 power equals one
5-6 = 1 = 1 answers may not be left with negative exponents
56
n6
15625
Other Examples:
2
4
 2
2 2
B)   =      =
9
 3
3 3
A) (.4) = .4  .4  .4 = .064
3
2
2
3 3 9
1
 1
 3
C) 1         2
2 2 4
4
 2
 2
D) (-4)3 = -4  -4  -4 = -64
Find the value of the following. Show all work.
1. 92
1
5.  
 10 
 2
9.  
 3
2. 10-3
3. 54
6. .25-3
 2
7.  3 
 5
3
3
10. (-1.1)
4
8
11.  
9
4. 0.37
3
1
8. 3.710
8
12.  
9
1
Date ___________________ 1E
Order of Operations
Name ___________________________________
Algebra I - Pd ____
When an expression has more than one operation, the order which we solve this is
very important. Take for example the expression 5 + 3  2
One person may do:
Another may do:
5+3 2
|
5+3  2
=8  2
|
=5+6
= 16
|
= 11
How do we decide who is right? To avoid confusion, we use PEMDAS.
Parenthesis
Exponents
M/D Multiplication/Division
First we solve any expressions inside parenthesis
A/S Addition/Subtraction
Finally we look for addition and subtraction from
left to right, solving whichever comes first
Second we simplify any exponents
Third we look for multiplication and division
from left to right, solving whichever comes first
Evaluate: 28  4  2(8  7) 2  5  3
= 28  4  2(1) 2  5  3
= 28  4  2(1)  5  3
= 7  2(1)  5  3
= 7  2  5 3
= 7 - 2 + 15
= 5 + 15
= 20
Parenthesis
Exponents
Division
Multiplication
Multiplication
Subtraction
Addition
121  3 2
, we must assume parenthesis. This expression
27
(121  32 )
2
can be written as (121 - 3 )  (2  7) or
. You must remember to simplify the
( 2  7)
numerator then simplify the denominator. Your last step will be to divide.
Note: When given an expression such as:
Evaluate the following examples:
1. 15 + 3  2 - 8
4. 2(7 + 3)(7 - 3)
7. 7 - 3(4 - 6)
2. (3 + 2)  4
5. 5(3)2 + 2
8. 20-23(-3)2
3. (18 - 12)  3
6. 3 + (5)2 - 2(-4)2
9. (3 + 5)2 - 2(-4)2
Name ___________________________________
Algebra I - Pd ____
Date ___________________
Evaluating Algebraic Expressions
When given an algebraic expression with one or more unknown variables, we can not find the
exact value of the expression. If we are told what the value(s) or the variable(s) are then we can
find the value.
For example:
13x + 2y
Since we do not know the values of x & y we can't simplify
If we are told to evaluate 13x + 2y when x = 3 and y = 4, we can substitute these values in.
First Step: Write the expression
Second Step: Replace variables
Final Step: Simplify using PEMDAS
13x + 2y
13(3) + 2(4) always use parenthesis
39 + 8 = 47
Errors often occur due to sloppiness and laziness, so be careful and be neat
Evaluate the following:
1) 50 - 3x when x = 7
1) ___________
2) 2x2 - 5x + 4 when x = 7
2) ___________
3)
2a
+ (n - 1)d when a = 40, n = 10 and d = 3
5
4) (2x)2 - 2x2 when x = 4
3) ___________
4) ___________
1
2
5) ___________
6) r2 + 4s when r = 3 and s = 0.5
6) ___________
7) a2 + b2 -d2 when a = 8, b = 6 and d = 3
7) ___________
8) (3w - 2x)2 when w = 10 and x = 8
8) ___________
9) 3w2 - 2x2 when w = 10 and x = 8
9) ___________
5) x2 - 8y when x = 5 and y =
10)
5
(F - 32) when F = 86
9
10) ___________
11)
1
x( y  z ) when x = 8, y = 5 and z = 2
2
11) ___________