Unit 1.8!
Date: !___________
Exponential Notation and Order of Operations
!
The vocabulary is important. Know what each of the
pieces and parts are called.
3⋅ 3 ⋅ 3⋅ 3 = 3 4
!
!
!
Factors!!
Base!
exponent/power
Ex. 1)! Write exponential notation for 10 •10 •10 •10
Ex. 2)! Simplify
!
a)! 5 2
!
2
−5
(
)
b)!
!
3
2n
(
)
c)!
Exponential Notation:!
!
b n = b⋅ 
b ⋅
b…⋅
b
n factors
For any NATURAL number n
Order of Operations.
Consider:! !
4+2×5
=
4+2×5
In order to ensure that the same value would be reached by
everyone, rules have been established.
!
!
1.! {[( )]} <-- •-->
!
Grouping symbols from innermost outword
!
!
∧
2.!
!
Radicals and powers
!
!
3.! × ÷
!
Multiplication and Division
!
!
4.! + -!
!
Addition and Subtraction
Ex. 3)! !
15 − 2 ⋅ 5 + 3
Ex. 4a)! !
(3 ⋅ 4 )2 ! !
!
!
b)! 3 ⋅ 4 2
!
Ex. 5)! !
2
−x
(
)
Evaluate
and −x 2 when x = 5!
!
2
−x
≠ −x 2 for all values.
(
)
We just showed that!
Ex. 6)! Evaluate −15 ÷ 3(6 − a ) when a = 4
3
Ex. 7)! Simplify
[
8 ÷ 4 + 3 9 + 2( 3 − 5 )
12 ( 9 − 7 ) + 4 ⋅ 5
2 4 + 32
Ex. 8)! Calculate!
3
]
Simplifying and the Distributive Law
!
Values trapped inside grouping symbols are effected
by whatever is directly in front of them.
Ex. 9)! 5x − 9 + 2( 4 x + 5)
2
2
7x
+
3
x
+ 2x ] − 5x
[
Ex. 10)!
Consider ! ( −1) ⋅ (5) =
( −1) ⋅ ( −3) = !
!
!
The product of (-1) and any number is the opposite of that
number, ( −1) ⋅ a = −a ,
!
and can be read as “the opposite of a.”
Ex. 11)! Write an expression equivalent to
− ( 3x + 2y + 4 )
The Opposite of a Sum: −(a + b ) = −a + ( −b ) = −a − b
Ex. 12)! Simplify:!
3x − ( 4 x + 2 )
Ex. 13)! Simplify:!
5t 2 − 2t − ( −4t 2 + 9t )
Ex. 14)! Simplify:
a)!
3n − 2( 4n − 5)! !
!
3
3
7x
+
2
−
5
x
− 1) + 8]
(
[
b)!
Note:!
!
!
!
!
We have been simplifying lots of different stuff
!
Simplifying a fraction means
•! eliminate any factors common to both the
numerator and the denominator, aka: Cross
out the matches or reduce.
!
Simplifying “polynomial expressions” means
•! clear any parenthesis
!
•! collect any like terms
!
Homework:
!
!
1-113 EOO (or more if needed)
Review beginning on pg. 75, Odds
In case you haven’t checked out the book thoroughly, please
note the Study Summary on pages 72, 73, 74 &
75. It does a great job of hitting all the highlights
for the chapter.